Why would the turn signal socket melt on a 1998 century?
I think it could be due to geometrical shape of the electrical contact at the socket or housing If the contacts are in an arc shape, it might reduce the surface contact to a very narrow point which will overheat by lack of material for heat dissipation. the overheat situation will create a spark at the contact which will create some carbon deposit which will increase the contact resistance inducing more heat until melting. Fred
On the 1997, 1998 GMC Yukon, the tail light socket, especially the right rear turn signal socket, tend to experience faster wear/ corrosion. Try using a non-conductive compound like painter's caulk while reseating/adjusting the bulb till it works. Let it dry in this position, then reinstall the fixture. Alternatively, replace the light socket module.