Engine swap - alternator query

I've just changed out the motor on my working (grass cutter) MTD mower. It's now a quiet (whatever that means) 12.5 hp Briggs engine. The previous motor was a 12hp unit. On the repacement unit I only have  one wire (red) coming from the motor wheras the old unit had a two pin connector (red + white). Am I right in thinking that I just need to connect red to red and ignore the white wire?

Maybe a pic can help. Should have been at least 2 wires. (possibly 3-4) One for charging, one for the Kill. (Possibly a headlight (accessory) power, and/or carb Solenoid depending on age)

Post the model number of the engine and I'll track down a wiring diagram for it so we can be sure. Which tractor are you working on, the yellow Dakota (MTD) we've talked about?

No, it's not 'The Yellow Peril', annoyingly everyday stuff has kept me away from getting on with that. The one I'm dealing with is the green 93 MTD I use for actually cutting my grass. I've changed the motor because to old one was going through so much oil it could have been a two-stroke. I'll pull it apart and seewhat I can do with it.
Anyway, here's some photos of what I'm dealing with. There isn't any fuel cutoff on the carb.

Sorry for the delay!

On the tractor white/red connector:
- the white wire is for the headlights (please confirm by following  the wire and if all looks good jumper 12v+ to it and turn the headlight switch on.
- the red wire SHOULD be the charge wire, confirm by follwing to the key switch, it should go to B post.

On the engine side of things:
-the pic is blurry and i can't tell if theres anything on the end of the wire like a connector.
- the block behind your hand looks to be the 2 wire, 9 amp voltage regulator. The red wire with the funny clip is most likely the charge wire, not sure about the yellow wire yet or the red wire in your hand... where does that red wire lead to? Under the fan shroud? I wonder if someone rewired the kill wire with that?

If you know what tractor the engine came with please say so, I want to look at the wiring diagram for that tractor. If not I'll try a long search and see what i come up with.

Yellow wire should be from the 5-9amp alternator.

Like @Brianator mentioned, the red wire from that module (Regulator) on the engine is charging.
And the rest of what Brianator said as well.
I agree the White is probably for lights "power from alternator" Old engine probably had a matching 2 wire plug.  You can ignore the white wire and if you need lights, run power from the battery to the switch.  

Is the blurry wire in your hand go to that plug further back and following the red into the little box (regulator)?  If so, you can connect that to the red in that plug if like Brianator says goes to the switch.

Well it looks to be confirmed that you were right @Normandybrit, the red wire coming off the VR with the red connector to the red wire on the tractor harness (for charge). If you want to get the headlights working you'll need to run a wire from the battery to the input side of the headlight switch, a 5amp inline fuse should be sufficient protection.

So tricky to solve electrical when not in person, takes me about as long to write a post as it would for me to figure it out with a multimeter in hand!

**Edit**  It appears that @MightyRaze was editing his post as I was writing mine and we've now basically said the same thing! Lol. Great minds think alike eh!?

Many thanks to both of you for your help! I'll connect that up later today and then we'll see if this replacement motor is as good as the seller says it was!