Placement of motorcycle for towing

The best place is - over the axles.

That 1200lbs … is it just the one motorcycle or two of them?

Agree, unless it is a very small toyhauler, it likely won’t make a huge difference, except toyhaulers are generally tongue heavy without a load in the garage, so you may find loading it as far rearward as possible will do the most to combat excessive tongue weight.

Pin weight, or tongue weight, won't change that much with just a motorcycle, independent of placement.

I've done all of the weight measurements and vehicle placement.
The biggest item to change pin/tongue weight is water or no water.
My sand rail is 3000lbs and the pin weight in my 5er is still 3600lbs with the motor/trans hanging 5' behind the rear axle.
My water tanks are 80% in front of my front axle and I always tow with full water.

Generally, the garage is already in place, so you don't really have a choice.

Yes, 1200lb can significantly impact the hitch weight. The further behind the axles, the more it impacts. They usually design toy haulers with higher hitch weights, so when it loses weight due to loading, it's still got a decent percentage on the hitch.

Also, a big 5th wheel is less impacted than a smaller travel trailer. A big 15,000lb 5th wheel, likely starts around 3000-3500lb hitch weight and the axles are set further back, so if a 1200lb bike takes 400lb, off the hitch, it's still got 2600-3100lb (17-21%) on the hitch. That's the lower end of acceptable but still OK. A 6000lb bumper pull is likely starting around 700-900lb hitch weight, so if you lose 400lb, it's down around 300-500lb (5-8%) on the hitch. That's in the range where stability becomes an issue while towing.

pjs1660 what type of toy hauler are you looking at? Bumper pull or 5th Wheel? Any idea of length yet? For the vast majority of Toy Hauler owners there is very little impact on the tongue weight of the larger haulers, but it does vary so knowing what you are looking at helps.

There usually isn’t going to be a whole lot of options. If you are happy with your tongue/pin weight directly over the axle is best. If you’re needing to add pin weight move the bike as far forward as possible …. move it back to reduce pin weight. My bike and carrier weighs about 1000 lbs and is about 17 feet behind the centre of the tandem axles. That is about the worst place to carry that much weight but it works. My rv handles noticeably better without the bike.

Have to assume you’re getting a towable and not a 5ver. I’d assume their tie downs are placed for optimal loading.I’d think it’d be set up more over the axles. On my 5ver, I keep it in the center of the garage and the weight is behind the axles. However, pin weight is essentially the same whether the bike is loaded or not.