87 Toyota 22R fuel / ignition question

[87ToytotaGuy]

I have rebuilt the 22R w/ some LCE components and put a Weber carb on it, I commonly have trouble cranking, meaning it takes a minute or two of cranking until it seems to fire up, like fuel pressure takes a while to build? When I kill ignition it will run for a second or two and turn over a few more times than expected before finally slowly stopping.

I am considering changing fuel pump to electric to be able to turn on with a switch before hitting ignition.

Has anyone encountered this before? I do not believe this occurred prior to engine rebuild/ switch of carb.

Thank you