Regards the security, if you have a non security turn signal module, then that's unlikely to be your issue.
I think the first thing to try and find out is if you are not getting fuel or spark...or possibly both.
I assume the bike was generally working fine before the primary and trip switch work?
Did you check the old trip switch to see if it showed continuity across the two wires with button pressed? It might not be the button that was at fault.
Does new trip button work in terms of switching between mileage and trip counter display with ignition on?
With ignition off and pressing trip button, does the odometer display mileage and the back light light up?
So the speedo won't preform a WOW test either?
With ignition on, does the engine light come on for 4 seconds and go out? Does it come back on and indicate current or historic dtcs? Will come back on for a few seconds for historic or stay on permanently for current dtc.
Does the fuel pump run for a few seconds when ignition is turned on?
Try checking for spark. You'll need to leave spark plugs in heads and use either a spare plug or a proper spark tester on the ht leads.
Try opening the throttle slightly just in case your IAC isn't working. If it's in a fully closed position and not operational it won't allow air through the throttle body.
If no sound of fuel pump priming, try swapping your start relay and system relay over.
I take it the fuses are good?
Check your fuel pump connector under speedo console is connected if console was disconnected to do trip button.
If fuel pump primes and you have spark, make sure fuel line is connected.
Check the earth connections in front of the battery attached to the frame by back of fuel tank.

Looking at some of the above general suggestions might help pinpoint a more focused area to address.

 

 

Okay, so the bike was fine before, and the fuel pump plus engine light cycle at key on.

Does the engine light indicate dtcs by coming back on, regardless of whether you are able to access them just now? I presume the trip button problem was previous to your current issue but obviously now it doesn't help you that you can't access any possible codes.

Thinking of relatively easy things to check before you have to go more in depth and also that you were working around the inner primary area.
One sensor that is in that general area that would definitely prevent you from starting the bike is the crank position sensor. It wouldn't stop the engine light and fuel pump acting like normal at ignition on and it'd allow you to crank the bike over, which is the situation you have. Whilst cranking though, it would prevent both spark and the fuel pump from restarting but it would in most cases show a dtc. Does the engine light come back on while cranking?
So it might worth taking a close look at the wiring and connector to the sensor down at the front of the primary in case it got damaged or the block connector got dislodged.

I see you have another thread going and there was a suggestion to check Harley's site , if you have no luck on HD's Service Information Portal regards information on your TSM, or possible TSSM you can always remove the rear fender plastic splash guard and look at the part number on the unit itself and then do a google search with your findings. It should be located on the plastic caddy behind the oil tank.
Also you should be able to at least access wiring diagrams for your bike which will help you if you have to start doing some proper electrical checks.
The HD electrical diagnostic manual would be the best thing to have if it isn't something visible and you find yourself having to do more detailed work.