buying used car - how does it work with insurance?

You have to agree the sale, sign the contract, pay for it, and go and pick it up with all the correct paperwork before you can "drive it back to Brussels".

I wouldn't trust a seller who has "already done" the seller's CT - not on a long weekend, and the earliest he can do the CT will be monday. Which will leave you time to call your insurance broker and ask them what to do.

I'm not sure why J 'wouldn't trust a seller who has "already done" the seller's CT'. Doing it in advance of a sale is not normal but certainly not unheard of - the car that I am currently using had a valid seller's CT when I went to look at it. So long as the seller produces the correct paperwork it's fine.
However, as to the original question, a car being sold will not have a number plate so that has to be organised in advance and the insurance on one car does not allow you to drive another without the insurers first having been made aware of what is planned and giving their approval. It used to be that you could take the plates off one car and put them on another to cover this precise situation but I think that this is no longer allowed.
All you can do is talk to your insurers - or get the seller to bring the car to you and then drive him/her home.

kasseistamper is right on all counts. Just make sure there is still enough validity in the seller's CT to complete the procedure before expiry. Also, last used car I bought I made a down payment and paid the balance when I picked up the car. How much of a down payment is a matter of negotiation. I whittled it down to 300 euros.