2 out of the last 3 days, I had a cold start problem with the Del Sol. It would crank fine, catch, and die immediately. It did this twice times before it stayed running on the way home yesterday.

I started to suspect the fuel pump, so this morning I put the key in "run" for a second or two to prime the pump before I turned the key to "start" today, and it started without incident. I also made sure to keep the key turned to "start" for a bit longer than normal.

Does this sound like a fuel pump to you all?

Sounds like the main relay. its a common issue

I'd check the main relay, but if you could hook up a fuel pressure test gauge to the service port (depending, on the Civic it's the top bolt into the fuel filter 'post' filtration line to the injectors) so that when you start the car you can get an idea of pressure readings to see if its within FSM specs on the vehicle is running.

I'd suspect a clogged filter or main relay before the fuel pump. Especially a starting issue if you can hear the pump prime itself with the KOEO and you can verify the pressure reading gets to spec with the first KOEO cycle. If I'm remembering this correctly. It's also possible to check the FPR at this time by disconnecting the vacuum line to the IM from the regulator, pressure should rise with its vacuum removed.

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'92 Civic VX, Canadian model