Those ring’s straps come in from the bottom of keepers, thru keepers and buckle onto the side buckle above blinker, on cheek pieces. There is a hole in the strap which goes over buckle tongue, then the strap from bridle crown comes into buckle and everything is held down when the strap end goes down thru the keepers or boxing.
Ring itself usually ends up by the blinker. Strap length allows trimming to shorten for fit to various size heads, so ring ends where you want it on the side of the horse’s head.
You can do a search on here, find old Tandem posts. I bumped up a couple I found which might have details you will find informative.
Carriage tandems usually have a roller in the Wheeler terrets. There are newer terret designs appearing, we haven’t used them. You do want terrets large enough, (Roger rings also should be big, open) so that reins moving fast don’t get hung up with a twist or too wide for small openings.
I strongly suggest you get some Tandem lessons from a professional before you endeavor to put your two animals together. You need to learn how to “pull a loop”, handle 4 reins at once, develop hand strength for all those reins, along with being able to give signals to each individual animal.
A reinboard setup, would be immensely helpful to you. You can build your own and practice rein handling, whip handling, in the house on cold days. Watching the weights move about when you move a rein, may help you get a better vision of what your horse is hearing with that rein tweak. Tandems out of all the Multiples, “over-respond” the most and the fastest. Rein length and weight to the Leader, can feel like you are shouting the signal by just moving your fingers tighter! You NEED to be able to do all the rein work without looking down to adjust things. You will wreck if you need to be looking down to drive your Tandem, no time to look and adjust hands, with their reaction time and length of turnout.
Do remember that a Tandem is considered a Multiple in Driving, with two animals out front. This means you ALWAYS have an able bodied person to ride with you, be handy when you drive them. Things can go so bad, so FAST you can’t imagine it. Driver can’t fix things by herself then. Nice horses are great to have, but this is all new to them as well, so they may not be at their best for a while. Even VERY experienced Drivers don’t EVER take the Tandem out alone. This includes RING WORK or down the driveway. Have someone at hand or riding in the carriage when you get two animals out to drive.