You can't expect to get alot of responses within, say 1/2 hour of the original post.
It sounds more like the overvoltage protection relay, possibly just the fuse on top of the relay, I'd definitely start there first, especially if it's more likely to do this when the engine is cold.
Another possibility is a bad engine temp sensor.
The OVP is located behind the black plastic panel behind the battery, it has a flip open lid with a red 10 amp fuse under the lid, check that fuse. Is the ABS light also on? If so, I'd replace the OVP even if the fuse is OK.
Do a search on OVP or "overvoltage", lots of clues there.

Gilly

ps Most fuel pump relay problems I've seen were tow-ins, that is, no start at all, dead relay.