The seal on the worm shaft may be worn out and in need of replacement after 33 years. The antenna arms and sector gear along with its grease would have shielded the seal from becoming UV damaged by the sun.
What really are you long term goals here? Eventually replace the antenna or leave it without? You can block it off the cavity with a piece of aluminum or PVC trim board sealing it in with marine sealant such as 3M 4200 if you want it to be more easily removed or 3M 5200 if its intended to be somewhat permanent and then caulk in between the baseplate and swivel head.
You can also just contact Wineguard about getting the new seals and bushings. There are rubber o-rings in the worm gear shaft itself and a rubber o-ring and nylon bushing to seal the rotating mount to the base plate both of which may simply be worn out. That mount is still being used and parts are available for it from Wineguard and their distributors. You may also be able to remove the mount and match up the o-rings and find bushing material at places such as ACE Hardware.
Even today in the Digital World the Sensar IV which already has the UHF wing mounted on it is about the best RV TV antenna available and a relative bargain at less then $150.