First suspect and a place to look is the system relay. It turns on the ignition and fuel pumps after the ECU sees the engine crank.
It is a white relay up behind the glove box.

The solder traces inside go bad or the connector terminals become corroded and sometimes it can be a grounding wire from it to the body that goes bad. You can reflow the traces as that is the fix in most cases.
Take a look at the windings for any discoloration and any odd burnt smell about the relay upon first opening it too! The coil may be losing some windings and will cause it to lose it magnetism to pull down the contact fingers.
Inside there are two separate contacts that have to close and sometimes they may not.

We all know time takes a toll on the weakest link.

The next link, is the fuse panel and fuses 4 and 6. Clean them good and use something to keep them from corroding.

You can pop open the cover as it slides upward after spreading the sides slightly. Observe the action inside when you turn the key and crank. If you hold one side down you will hear the pumps run. The other side is ignition you won't hear anything. If either are lazy in closing then that maybe the delay you are having.

It is worth a shot anyways!

Phil