Yep, there’s your problem. The pcm is making the relays click like that (for whatever reason, I do not know). But it’s doing it because the capacitors are bad which greatly increases how long the computer takes to get ready to start. If you wait long enough, CEL will come on, relays should stop clicking, and it should start right up.
capacitors are soldered to the circuit board of the PCM. The project requires taking out the PCM, opening it up, cutting into the circuit board insulation, removing the old capacitors and soldering new ones in place.
if it were me, I’d turn to eBay. There are many sellers on eBay who will let you ship the PCM to them, they swap your capacitors, and send it back for around $100. Pretty common issue for YJs at this age.