Hi
I am sorry Finn has MUO, and it is great that he has responded so well. this is really positive news.
As with all autoimmune/immune-mediated diseases it isn't until the drugs are considerably reduced or withdrawn that anyone knows if a relapse will occur. If a dog is not in true remission he may relapse when the drugs are at a low dose or within a month or so after the drugs have been withdrawn. If this happens then the drugs have to be reintroduced or the dose has to be raised, usually up to an immunosuppressive dose. If the dog doesn't relapse and time goes on and the dog is still well then he has reached remission.
To develop an AI disease a dog is born with a genetic predisposition to autoimmunity. This potential cannot be detected until something within the environment such as drugs, vaccines, preventative treatments (wormers/flea spot -ons etc) stress or hormones, triggers the immune system to wrongly attack a part of the dog's own body. So long term remission - hopefully for life - is all that can be hoped for and all the owner can do is to limit, as best as possible, the trigger factors.
When Finn finishes his treatment, it is hoped that he will be in remission - and his clinical signs and blood results will indicate this. Personally, I agree with you. You know Finn's diagnosis, and you are aware of the clinical signs. If Finn is well then I see no reason for you to consider a spinal tap, and if a spinal tap is performed whilst the dog is on preds it may not be a true analysis, because an elevated white cell count may not be seen in an immunosuppressed animal/person.
If you have a concern, because Finn is exhibiting certain clinical signs, then you can have a blood test done and nothing else is obvious (it could be something unrelated to AI) and the clinical signs are as before then you can assume a relapse and start treatment all over again.
Checking blood results every now and then might be comforting, but to put his body though the stress, and the potential trigger, of a General Anaesthetic for a spinal tap might not be a good idea, especially if he is well in himself. This is a good link:
https://www.fitzpatrickreferrals.co.uk/neurology/meningoencephalitis-of-unknown-aetiology-mua/Jo
P.S. If you are worried about telling your vet of your decision not to have a spinal tap, just say you can't afford it. It works every time!