There is only one vacuum line to the modulator ,and it needs to be hooked up to manifold vacuum...(strong suction at idle,less when you rev it up)..best to use the stock fitting and location if you have the original manifold still...
When a modulator loses vacuum or the diaphram in it fails,the transmission will stay in first a lot longer,then shift harsh into second,and may not want to go in third at all,or feel like it free wheels when you let off the throttle instead of going in third..
If you see any ATF in the vacuum hose it is an indication the modulator's diaphram is ruptured and this will let ATF be sucked into the engine ,eventually lowering the fluid level enough to cause issues.the modulator can affect reverse and line pressure,cause slippage,hard shifting,etc..
I think leaving the vacuum hose off the modulator increases the line pressure,that may account for reverse "working" better with it off- -----reverse is usually the first gear to lose in a TH350 when the clutches are about done,and higher pressure might apply them tighter and make it slip less, or not at all..
The only other thing a TH350 has is a detent cable to downshift it when you floor the gas pedal...it needs to be set right,if its too tight it'll tend to prevent it from going into third or staying in...but it would have no effect on reverse as far as I know..sounds like you may be losing one of the clutch packs or possibly a valve body issue..
I have never gone farther than trying a fluid & filter change,a new modulator ,and adjusting the detent cable on the TH350's I have had--never had the nerve to try taking one apart or rebuilding one,I just put in another good used one...
Greg Ducato is the man to diagnose it here!...