I am renovating an old building with a toilet and when that toilet was originally installed it used what appears to be a non-standard setup with a tank close to the building and a vent tube going right up out of that tank amd no vent in the pipe draining the toilet. So that ends up not being super reliable in that the toilet flushes slow and I assume that is because of inadequate venting. I want to tap a small vent into the 4” pipe below the toilet and then run that into the main vent coming out of the outside septic tank up above ground level. I know that is all a bit odd, but my question is: is there a way or product that allows me to go a foot or two below the toilet and drill right into the 4” pvc and add a 1” pipe to vent the toilet? The 4” toilet drain pipe is at a 45° angle, so I can come out of the top side of it no problem, and no liquid will flow into the vent pipe, but the connection needs to be gas tight to keep the stank in. How can I make that connection without removing the pipe, that is to say, can I just drill and add a smaller DWV pipe to it? How would I do that so it is sealed?
Thanks for any help!

Saddle fitting is what you are looking for.

Not much to post for pics, but yes I am certain that the main vent in this case is from the tank itself. My uncle and his buddy built it, uncle remembers it. He says is has over 120 feet of leach pipe in sand/gravel, and it has never backed up, just often flushes once real slow without emptying the toilet, then a second flush when tank refills always flushes great.
It is a split system with greywater in one tank and black water in the other. The toilet is the only fixture on the black tank. So it runs out of the toilet into a 4” pipe, at angle through concrete footer and directly into the buried tank, and that tank is vented. I think maybe foam or something is slowing the venting either at the vent outlet or 4” pipe inlet. So the first flush gets the air moving and gets the foam out of the way and second flush is free to vent properly. But I am asking here because I am not a plumber and all of that is an uneducated guess based on no experience or real understanding of what might be going on. That is to say I am well aware I am likely wrong.

Every fixture should be vented within 5-6 feet, code allows some exceptions. How far is your toilet from tank & vent? I have similar setup for my garage it works well, but my 4" vent/ cleanout is only about 4' away outside. Saddle fittings aren't permitted in most areas and you want a minimum 1-1/2" vent size. Sometimes in the winter hoar frost will form inside undersized vents through roofs plugging them, as mentioned the toilet itself could also be the problem. The trap could be siphoning and the first flush refill, second flush clears it. Maybe an older 3 gal per flush toilet somebody changes the guts to 1.6, all kinds of different possibilities.

what snyde said, vent needs to be close to fixture, can you cut into line outside by wall and put a tee, in and run your vent up the outside wall?

Thanks for the suggestions. It is a 1-1/2” vent, but it comes right up out of the tank, and is probably 10 feet away.

I guess all I can do is saddle onto the 4” pipe. Ugh.