66 transmission emergency! please help

[SDGuy]

long story short- full exhaust system breakdown due to age (not replaced for about 30 years I'd say), thought it was causing my car problems moving around, etc., just had it replaced an hour ago

get home, there is a long hose hanging down- is this the air hose
for the transmission (it's not shifting correctly, and running hot),
if so,

WHERE DOES IT PLUG IN? I've crawled underneath, but simply can't find it. It comes from just below the air filter

automatic transmission, 66 straight 6

I have to go drive it right now, will check here later