I've noticed on my '89 that if I am using the rear tank, it's hard to start. If I use the front tank, it fires on the first turn. Fuel pump? I am about due for a filter change, but I think both tanks flow into the same filter, right?
It runs fine, no issues, which is surprising considering I'm still running the original cat,original fuel pumps, original ignition module, ect.

 

The pump in the rear tank might be getting a little weak and isn't priming the system enough on initial startup. Try cycling the key 2 or 3 times before starting and see if anything changes.

 

Throw a fuel pressure gauge on it and you'll know better what's happening.
The high pressure pump should be delivering high pressure no matter which lift pump is feeding it.
Unless the lift pump isn't lifting enough to feed it; or there is a restriction in the rear line or pickup; or there could be a power issue when the rear tank is selected.
Just changing the lift pump might fix it; but it could be a waste of time as well if the problem is something else.