Green wire is for the Neutral Solenoid, and the Blue, is Reverse Solenoid, but both actually have to be energized to get Reverse
Check for Continuity between each wire and Ground.
You really need to get the proper Service Manual before you go ripping one of these apart. Yes, if someone has worked on these for years, they probably could work on them Blindfolded, but...
If water doesn't drain out, and the old Oil doesn't look like Irish Creme, the gearcse seals are likely good, replace the Washers on the Drain/Level Screws.
Make sure to use a Type C Oil that is useable in Units with Electrical Components, Some 3rd Party Oils aren't. OMC/BRP markets it as 'Precision Blend.
Once new oil is in, apply power to the Green wire and rotate the Driveshaft, rotated fast enough, the Case should shift into Neutral, applying power to the Blue too, and continued rotating the Driveshaft, should shift it to Reverse