Gen 2 T3 - Starting Issues

I've recently had an intermittent issue getting the car started as follows -

The car unlocks, but no dash lights are on. Putting the key in the slot and pushing the start button has no effect and the car is basically dead. However after 5-10mins, the car seemed to burst into life on its own an could be started as usual. This has happened twice in the last week, but the car has otherwise been normal.

First time, the car was being started from overnight, second time, the car had been sat for about 90mins.

12v battery was changed a year ago - checked today and found good with plenty of charge.

When the car was finally started, the clock had reset, but the radio pre-set channels were still present.

100,000m service was carried out at Toyota in December with no issues.

One other issue - had a headlight changed due to opiacity. This was done in late December and I think the headlight now has a loose connection and will not turn on when the other one does - however giving it a bit of a thump, or driving over a bump will get it working.

Any suggestions on what the cause of this non-starting issue might be would be appreciated. The car has been 100% reliable and has never let me down since I bought it in 2014, so its a bit of a shame it's doing so now, just when I've spent a load of money on it!!