implement _index_data parts of #24024
Besides narrowing down the scope of #24024, I _think_ this might fix the segfaults I had in my old DTA branch, which may make it feasible to hugely simplify the composition changeover.

Aside from removing apparently-unused imports in reduction.pyx, the affected code is copied verbatim from #24024.
Hello @jbrockmendel! Thanks for submitting the PR.

 - There are no PEP8 issues in the file [`pandas/core/indexes/base.py`](https://github.com/jbrockmendel/pandas/blob/350b0ecdf11c18c40dbc7fed0082240add8ae047/pandas/core/indexes/base.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/datetimes.py`](https://github.com/jbrockmendel/pandas/blob/350b0ecdf11c18c40dbc7fed0082240add8ae047/pandas/core/indexes/datetimes.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/period.py`](https://github.com/jbrockmendel/pandas/blob/350b0ecdf11c18c40dbc7fed0082240add8ae047/pandas/core/indexes/period.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/timedeltas.py`](https://github.com/jbrockmendel/pandas/blob/350b0ecdf11c18c40dbc7fed0082240add8ae047/pandas/core/indexes/timedeltas.py) !

 # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=h1) Report
> Merging [#24379](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/5d134ec1a9ab118abbd16157bd161783547117e6?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24379/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #24379      +/-   ##
==========================================
+ Coverage   92.29%   92.29%   +<.01%     
==========================================
  Files         162      162              
  Lines       51841    51845       +4     
==========================================
+ Hits        47847    47852       +5     
+ Misses       3994     3993       -1
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.7% <100%> (ø)` | :arrow_up: |
| #single | `42.98% <100%> (-0.01%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/24379/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9wZXJpb2QucHk=) | `93.11% <100%> (+0.01%)` | :arrow_up: |
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/24379/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `96.33% <100%> (ø)` | :arrow_up: |
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/24379/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `96.27% <100%> (ø)` | :arrow_up: |
| [pandas/core/indexes/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/24379/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy90aW1lZGVsdGFzLnB5) | `90.44% <100%> (+0.02%)` | :arrow_up: |
| [pandas/util/testing.py](https://codecov.io/gh/pandas-dev/pandas/pull/24379/diff?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvdGVzdGluZy5weQ==) | `87.66% <0%> (+0.09%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=footer). Last update [5d134ec...350b0ec](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=h1) Report
> Merging [#24379](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/5d134ec1a9ab118abbd16157bd161783547117e6?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/24379/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #24379      +/-   ##
==========================================
+ Coverage   92.29%   92.29%   +<.01%     
==========================================
  Files         162      162              
  Lines       51841    51845       +4     
==========================================
+ Hits        47847    47852       +5     
+ Misses       3994     3993       -1
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.7% <100%> (ø)` | :arrow_up: |
| #single | `42.98% <100%> (-0.01%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/24379/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9wZXJpb2QucHk=) | `93.11% <100%> (+0.01%)` | :arrow_up: |
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/24379/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `96.33% <100%> (ø)` | :arrow_up: |
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/24379/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `96.27% <100%> (ø)` | :arrow_up: |
| [pandas/core/indexes/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/24379/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy90aW1lZGVsdGFzLnB5) | `90.44% <100%> (+0.02%)` | :arrow_up: |
| [pandas/util/testing.py](https://codecov.io/gh/pandas-dev/pandas/pull/24379/diff?src=pr&el=tree#diff-cGFuZGFzL3V0aWwvdGVzdGluZy5weQ==) | `87.66% <0%> (+0.09%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=footer). Last update [5d134ec...350b0ec](https://codecov.io/gh/pandas-dev/pandas/pull/24379?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 thanks!