I am referring to your first post PatO, I am pleased to flatter. Basically, I built your design exactly for testing. I got the delay to work for 90 seconds as your diagram stated. I want the inverter to stay on longer then 90 seconds to maintain power to the computer while I get gas or run into a store for a few minutes.
I figured that if 4700uf is good, 10000ufX10 is better! It turned out to be the case. I purchased the caps off of eBay for $21. I choose 25v because there are smaller then comparable 35v caps and there were what I could find on eBay

(I divided the 4700uf by the amount of time it maintained power, then just looked for enough ‘uf’ to give me ~7 min. Sloppy yes, but it worked, and this thread is called “ghetto”!)
On the contrary to it creating failure points, had I used only one cap, should that fail, the device is useless. Using many caps in parallel, if one fails, the delay is only shorter. Also, I am avoiding touching any of the wires, hence the box
So those caps do only power the relay, not the system. As I stated, it maintains the relay for over 7 minutes. The circuit is exactly the same, LEDs and all, except for the added caps for the longer time.
the realscott, sorry if my previous posts were confusing. I am new to the forum and am still not sure how the ‘quote’ system works so I just mentioned the diagram that I used. I thought if I used one more picture in my post I would be banned

I would love to help, but I am positive that if you saw the bottom of the circuit board, you would only be more confused! It is a mess, and was a pain trying the get all the caps connected and run into the circuit (a hint is that I ran jumper wires on top of the board as well as made solder traces on the bottom to get it all connected) It does work, and I suggest starting over from scratch, I ran into the same problem and just started over when it did not work the first time with new parts. Be sure that the base, collector and emitter of the transistor are correctly connected and the diodes and LEDs are facing the right way. Stoopid I know but it happens. Let me know if I can help any more (or did I confuse you more?)
Now I will wait for someone to reply “TL DR”