Brad, once you get the housing off the tach, you should see some small screws I think around the outer edge of the white plastic. I may be wrong, but I think those screws hold the unit onto the face plate and stuff. If it isn't those, then check the ones in the center of the back of the unit - those are the ones that had been JB Welded on your old tach so we couldn't pull 'em.
How do the wires look on the "new" unit?
Sorry, y'all; if that tach has any little screws around the edge of the white plastic, it ain't like any VN750 tach I've ever seen. I've got one apart in my hand right now.
The bezel is held on by that ¼" or so wide chrome ring at the junction of the housing and bezel. The chrome bezel itself is a cover for another inner metal ring with a gasket around the bottom edge and another wider rubber gasket at the top that holds the lens.
There's 3 ways I know of to get that narrow ring off.
One is to gently pry up the edge on the housing side a little at a time all the way around, then a little more, then a little more, until you get to a point where you can pop it off there. When you put it back together, you gently crimp that edge back down with a pair of channelocks with the jaws taped to keep from messing it up any worse than it already is. Beavis up in Tennessee did it with his.
The second way is to cut the ring. You do _not_ want to do this, unless you're willing to resistance-weld an L-shaped bracket to the cut ends, and bolt it together with a 2-56 or 4-40 bolt, nut, and washers. You'll end up with a gap of about 1/8" to ¼". The ring I've got here was broken in a wreck; the ends fit together, but not when they're wrapped around the bezel and housing. It ain't going together by hand, that's fer sure.
The third way is to send it to the factory and have them do it; they've got the tool that pops that sucker off and puts it back on in about 3 seconds. There's a dealership in Lincoln, NE, that has that tool, also; and apparently a _very_ few other dealers across the country. (There's actually prolly quite a few that have it, and don't have a flippin' clue what the tool is for.)
Billy Greer's odometer quit on him at ~72,000 miles while on a major trip around the U.S., near Lincoln, as it happens. It was either the Lincoln dealer or the factory that replaced the odometer for him; he told me, but I can't recall for sure which it was. (He did the factory tour thing on that trip)