Not a caddy expert but tracing all the vacuum lines should help you out..quite possible a vacuum line runs to the transmission.
The vacuum T usually runs hose from the distributor to carb..maybe to the charcoal canister and other accessories.
I would pull the trans pan and check for metal and other crud..change out the filter.
Don't over torque the trans pan on re install...the torque setting is probably 8-10 ft pounds.