a727 no third gear

Make absolutely sure it full of fluid by checking in neutral.
Then I would pull the pan, check for debris.
Then pull the VB and air test it because it sounds like and internal seal or sealing ring leak if none of the above.
Also if 2nd has some sort of issue where it can't apply the band it can shift directly from 1st to 3rd, so be sure this isn't what it is doing by putting the trans in manual second.

An FYI, a plugged or incorrectly installed filter can cause a no 2-3 upshift also.