13HP B&S cutting out when alternator plugged in.

The mower starts & stops ok. But will cut out when I engage gear & release break. Also when I engage the mower blade. But if I unplug the connector to the alternator works away but the off doesn't work then on the ignition until I plug it in. small problem but annoying me!!!

OKay - No beer in the house but got the Engine model number 28M707 type 1183-E1 off a Jonsered mower. Not the original engine.

Pour yourself a beer and look at what you just posted. Do we know what type of unit you have. Do we know which of the twelve styles of Briggs engine you have? Now that you have finished your drink, go out to the unit and get the model and serial numbers of the mower. Then get the model, type and code numbers for the Briggs engine. Post them and we can give you some good suggestions.

OK, you only get to stand in the naughty corner for 1/2 the time as you did give us the B & S number & told us it was a Johnsored.
This might be tricky as it could be a USA mower or a European import & the latter are hard to get information on.
Also very important,
Did you buy the mower new ?
If so when did it start to do this and what did you "fix" just prior to this problem manifesting itself ?

If it is a used mower, did it do this from day 1 or has it just started to happen ?

I got the mower recently off a neighbour, the engine was busted so got a guy to replace it. The mower is ancient guessing 17/18 years old. The replacement engine is old as well. I just put a new battery in, before that was runnnig without a battery with alternator unplugged, worked fine for a couple of cuts with the new battery but then kept cutting out until I disconnected the supply again from the alternator. I think it could be because its so old there is a loose/corroded connection or short somewhere. It will cut out when switch opened on level to engage the blades or when I release the break - I assume there's a switch on the break lever as well. I've been looking to get a wiring diagram but haven't found anything detailed enough yet to help buzz out the connections.

All tractor type mowers are basically wired the same
The PTO & Seat switch are wired together
and
the Brake switch & seat switch are wired together
Both of these circuits are hooked up in parallel to the magneto cut out wire.

None of them are connected to the charging circuit

Briggs have a nice little publication called the "repower guide" and another poster "alternator guide"
Google them and download both.
The alternator guide you will use to identify which alternator you have
The repower guide has the basic wiring diagrams for mowers.
You sound like a reasonably smart fellow so you should be able to work things out with these tools.

I will hazard a guess that the ground connections are bad and one or more of the switches are corroded beyond use.

Just one word of caution.
The magneto has a chip in it ( engines without points ) .
If 12V so much as looks at the magneto kill wire, it does just that, kills the magneto, good & proper, forever.
So when working on problems like this pull the kill wire of the magneto and check it for voltage for all combinations of the various switches before you hook it back up again, including engine running.
The brake & PTO switches have 2 circuits, one is a ground circuit that goes to the magneto kill wire, the other is a 12V circuit that energises the starter solenoid.
Different switches have the terminals for these in different positions but nearly all use the same 4 pin plug on the wiring so it is easy to cross wire.