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I'd personally paint all the connectors back there with some Stabilant 22, if I ever have to open mine due to the GPS issue (or any other issue, I'll probably do it since it would be open anyway.)
Stabilant is great in that it seems to really make marginal electrical connections much more stable, due to some materials magic.
It's expensive as shit, but since you use such tiny amounts it lasts basically forever and can help with any intermittent connection issues. I used it on my motorcycle for instance when installing accessories.
A tip for wonky electrical connections might be to use some of this stuff on connectors and the like. If the issue is intermittent connectivity it can most likely help.
It's expensive, but you dilute it with isopropyl and paint it on any connectors. I've been using it for a few years whenever I do electrical stuff, for instance putting accessories on my motorcycle. It's definitely going on all the connectors etc in my van also when I assemble the electric stuff.
If you want the GPS to work, buy some Stabilant 22, open the phone (easy to do with some care) and gently do the GPS pin bending fix and paint diluted Stabilant on the pins and the connectors on the rear shell. That should almost certainly sort it, unless you routinely sit on your phone and squeeze it together or something.
I mean, sure, if the pins bend back way too much when the phone is compressed so there's an actual air gap, then nothing will work, but if the connections are just iffy, Stabilant might just do the trick.
No clue off hand, but I would like to recommend picking up some Stabilant 22 off Amazon, diluting that with isopropyl and then painting all connectors and the like with that. It can help deal with crappy connections, if that's the issue. https://www.amazon.com/Stabilant-5ml-Kit-Makes-30ml/dp/B001E50GQS - it's expensive per volume, but probably worth a shot, and a tiny amount will last you decades as you don't use a lot per connector. I got some and used it on all connectors I've added on the bike just as a precaution.
Of course, another thing might be a broken cable or damaged harness that gets you intermittent connectivity. Have you tried gently pushing/pulling on the cable bundle and then trying the starter again?
What does the ECU itself say? Error codes?
If you don't have a TuneECU setup already, hit up http://www.lonelec.co.uk and buy the Triumph ECU cable kit (I recommend that specifically, as it's a known-good cable with the right FTDi chipset), and then install TuneECU from http://www.tuneecu.com on a PC (or buy the affordable Android variant off Google Play) and it will give you error codes and other data off the ECU, and lets you reset said error codes if they were transitory problems.
Have you cleaned the contacts? Cleaning it with rubbing alcohol 91% or higher could help. A long time ago I used to have stabilant 22 - https://www.amazon.com/Stabilant-5ml-Kit-Makes-30ml/dp/B001E50GQS/ref=sr_1_3?dchild=1&keywords=stabilant+22&qid=1633184540&sr=8-3 which I would squeeze a drop on a little paint brush and work into the contacts. That helped my 3DS's charge cable immensely.
But yeah, start simple. See if you can clean the contact first. If that doesn't work then maybe replace the charge cable.
You could try some Stabilant 22. It's magic for intermittent connections.
Expensive per weight, no question, but a little goes a long way.