Gonna be honest, conservatory roof leaks like these can be a right pain to solve. It is potentially the foam padding and silicone sealant that has ' let go ' , or it could be the main ridge cap , or even the junction of the main ridge cap to wall. ( i seen it from all three places but dripping from the finial undercap ) Water can penetrative anywhere and seep through various channels and exit at its easiest and lowest point.
Firstly you need to decide which side you think it is coming in , then as youbhave the inner cap of , see of there is any obvious places it could be running from , them unfortunately you will need to go outside, potentially removing the top cap to see whats going on...now tbh , I wouldn't remove yhe cap, I'd just be looking at resealing everywhere I can see that has had sealant applied previously, including getting up under the semi circular cap, just pump it full and push it in , as long as youbcant see it from the ground it should be ok .
Now before anyone jumps on me saying ' this is a botch ' , very few double glazing companies will evem get involved at looking at leaks on old conservatories, as suddenly any future leaks become their problem .. so they wont remove the capping outside, as it runs a real risk of creating even more leaks that suddenly became their problem in the future that they are expected to fix for free due to trying to solve this initial leak. Obvioulsy being your own conservatory you might want to remove the ridge to check, but depending on the system that may not be as easy as you first think..... hence why I say just reseal it and fill any areas with clear low modulus silicone where you think it may be leaking
Good luck ... you may need it
Ps ... i know it sounds like doom and gloom but trust me , old leaky conservatory roofs can be a nightmare but some can be an easy fix if obvious
