double check illuminated entry circuit

The blue/grey is already ignition controlled in the sense it will shut down immediately with door closed and ignition on (actually about 1 second). What if you're working on on the car, do you want those lights on for 10 minutes? Hence my battery coments. I would insert a 528t set to say 30 seconds or 1 minute then daisy chain 1 relay for the second circuit off that, diagram later I've some work for this morning. (Nearly 8:00 am in the UK).

More thoughts. Set the timer on the 528t for up to 1 minute. I've used these relays as "interruptors/changeovers". The reason being I believe you are feeding back into the ignition circuits. I might be wrong and if so try it by applying a fused 12Volt constant feed to both blue/black rev wire and RED / yellow h/light wire, not at the same time! If there's a tiny spark and the lights work without any ignition light-up you're good to go and you can substitute an 87b relay for the lower two relays. You could take it a stage further and cut the yellow 528t out put wire via an ignition controlled relay, 5 amp mini PCB or mini cube relay, ign. to 86 ground to 85 528t to 87a relay side to 30.

If the above works you can use a double separated make relay type 87b. Here's a part number from Tycho:- 5-1393304-6 U0/1 Form U