Pinout for this Microsoft Mouse's SERIAL to PS/2 adapter cable, is as follows:

SERIAL male con.__________PS/2 male connector
Pin1 ------------to----------Pin5 [Mouse Clock]
Pin5------------to----------Pin3 [GND]
Pin8------------to----------Pin4 [+5V]
Pin9------------to----------Pin1 [Mouse Data]

This adapter 100% works with the Mice that look like in the picture, that have a Motorola [SC88715DW] chip, and 7+1 wires in the cable.
Also recognizable by the following stickers (not 100% certain on 2nd sticker):

This PS/2 wheel mouse WORKS with all 3 of these SERIAL adapters.. yet, they are not the same!
I have tested them on a VIA MVP3 Mobo with Win98SE.

Here are their pinouts:

Grey Adapter:
SERIAL fem. con.__________PS/2 female connector
Pin1 N.C. xxx(Not Connected)xxx. Pin1 [M.Data] strapped to PS/2 Pin5 [M.Clock]
Pin2------------to----------Pin2 [K.Data]
Pin3------------to----------Pin6 [K.Clock]
Pin4[strapped to SERIAL Pin6]
Pin5------------to----------Pin3 [GND]
Pin6[strapped to SERIAL Pin4]
Pin7------------to----------Pin4 [+5V]
Pin8 N.C.
Pin9 N.C.

Red Adapter (identical to Gray adapter, but missing the strap between PS/2 pins 1&5):
SERIAL fem. con.__________PS/2 female connector
Pin1 N.C.
Pin2------------to----------Pin2 [Keyboard Data]
Pin3------------to----------Pin6 [Keyboard Clock]
Pin4[strapped to SERIAL Pin6]
Pin5------------to----------Pin3 [GND]
Pin6[strapped to SERIAL Pin4]
Pin7------------to----------Pin4 [+5V]
Pin8 N.C.
Pin9 N.C.

Green Adapter:
SERIAL fem. con.__________PS/2 female connector
Pin1 N.C.
Pin2------------to----------Pin2 [Keyboard Data]
Pin3------------to----------Pin6 [Keyboard Clock]
Pin4[strapped to SER.Pin6]--to--Pin1 [M.Data]
Pin5------------to----------Pin3 [GND]
Pin6[strapped to SER.Pin4]--to--Pin1 [M.Data]
Pin7------------to----------Pin5 [M.Clock]
Pin8------------to----------Pin4 [+5V]
Pin9 N.C.

The Gray Adapter design was also confirmed working by another user here that has it(@Jason21), on this other model:
2-button "Microsoft Serial-Mouse Port Compatible Mouse 2.0" P/N 58264:

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MICROSOFT branded adapter but with different pinout, found here on the forum. Comes in 2 different colors. No confirmation yet on what revision mouse it works with, but it did NOT work with the P/N 58264 mouse in the previous picture
Thanks to @Jason21 and @DaveDDS for their contributions!
Re: Microsoft Serial Compatible Mouse only works in PS/2 mode
Re: Microsoft Mouse 2.1A not recognized

Microsoft P.N.68666 Adapter(s):
SERIAL fem. con.__________PS/2 female connector
Pin2------------to----------Pin2 [Keyboard Data]
Pin3------------to----------Pin6 [Keyboard Clock]
Pin4[strapped to SER.Pin6]--to--Pin5 [Mouse Clock]
Pin5------------to----------Pin3 [GND]
Pin6[strapped to SER.Pin4]--to--Pin5 [Mouse Clock]
Pin7------------to----------Pin4 [+5V]

An unconfirmed adapter, pinout from user @Jason21. Unknown what it works with.
Microsoft Serial Compatible Mouse only works in PS/2 mode
Unknown-compatibility Adapter:
SERIAL fem. con.____________PS/2 female connector
Pin1------------to-------------Pin1 [M.Data]
Pin2[strapped to SER.Pins5,7]--to--Pin4 [+5V]
Pin3[strapped to SER.Pin9]----to--Pin3 [GND]
Pin5[strapped to SER.Pins2,7]--to--Pin4 [+5V]
Pin6 ------------to------------Pin5 [M.Clock]
Pin7[strapped to SER.Pins2,5]--to--Pin4 [+5V]
Pin9[strapped to SER.Pin3]----to--Pin3 [GND]

Another unconfirmed Blue Adapter, pinout from user @luRaichu. Unknown what it works with.
Re: Microsoft Mouse 2.1A not recognized
Unknown Blue Adapter (with possible unmapped "strap" for pinout)
SERIAL fem. con.__________PS/2 female connector
Pin2------------to----------Pin1 [Mouse Data]
Pin3------------to----------Pin6 [Keyboard Clock]
Pin4------------to----------Pin4 [+5V]
Pin5------------to----------Pin3 [GND]
Pin7------------to----------Pin5 [Mouse Clock]

This adapter is ONLY for the Microsoft SideWinder FreeStyle Pro and the SideWinder Precision Pro Joystick (but NOT for the SideWinder 3D Pro Plus, which looks absolutely identical), or the SideWinder 3D Pro, or anything else that didn't come bundled with it from the factory.

This is the Pinout:

DB15 GamePort fem. con.______USB-A male connector
Pin1-------------to-----------Pin1 [+5V]
Pin14------------to-----------Pin2 [Data-]
Pin10------------to-----------Pin3 [Data+]
Pin4-------------to-----------Pin4 [GND]
Pin2[strapped to GAMEPORT Pin7]

Pinout for this other adapter will be added later

Place holder -- probably for keyboards adapters

Place holder -- reserved for more obscure stuff that I can't think of RN

If anyone has any adapters that they're willing to map out.. or have any solid info on compatibility; please don't hesitate to share!
All contributions are welcomed! 😀