The swingarm is rubber-mounted and flexes in turns. Unfortunately, it's a real and serious problem. The specifics are thus:
As the bike leans into a turn, usually at extra-legal speeds, the rear swing arm's rubber bushings allow the swing arm to pivot laterally just a little bit and the wheel goes to the outside of the turn. The bike attempts to self-correct - its natural design and inclination wants the wheels to be in line, so the front end weaves out a little, which puts more stress on the swingarm pivot - rinse, repeat. The more severe your rear tire wear (flattened out from lots of highway miles), the more this problem is exacerbated.
Several "solutions" to the problem exist, the two most notable are the
Sta-Bo bushing replacement kit, and the
RideStr8 lateral link system. The sta-bo is a step in the right direction, but the outer rubber bushing should be replaced for maximum stability. Of course, people whine about the increase in vibrations, so it's kind of a no-win scenario.
I have experienced this in-lean wobble at some extra-legal speeds on big sweepers and I don't mind saying - it can be quite a wake-up call. The bike needs to have the rubber mount removed, replaced with proper bushings and bearings. If vibes are really that much of a problem, Harley needs to better isolate the engine from the frame. Or... as I've been saying for quite some time... put the "B" engine from the Soft Tails into the FLxx frames as they're so, so much smoother. That would handle the vibes and ditching the rubber would fix this problem. Viola.
Having said all that, you can mitigate the problem by exercising body-position steering modification by slightly "hanging off" in those intense turns and keeping the bike more towards vertical and farther away from that threshold at which the swingarm will lever out. You can also just take the sweepers slower.
These bikes are also pretty sensitive to having the steering-head bearings in proper adjustment.
PS... the one with the dual-headlight, frame-mounted fairing (highway bar mounted, actually) is the Road Glide. All of the Electraglides, street glides, road glides and road kings are mechanically identical, the differences being, primarily, appointments above and forward of the steering head. The road kings have tank-mounted instruments where all the glides have fairing-mounted instruments.
