What's that rattling noise in the video? I hope that it's not your bearings! (The good news is they can be replaced). Is there any vibration?
My Coronet CL3, circa 1988, is the same as yours, except for the colour.
The whole head-stock assembly, motor and all, is clamped onto the two base bars by one bolt through a banjo assembly - the one that's used for aligning the headstock underneath that should have a lever bar attached. The clamp also allows the head-stock to swivel.
Hopefully the threads and nut are in good order. The nut inside is held down within a recess on the casting. It's a good idea to check the state of the nut, the bolt threads and that the casting is intact at this point.
(That base index line on the front is advisory...... the true head-to-tail axis can very simply be got by aligning the points of both the drives, then locking the head-stock bar and position the tail-stock before you start work).
Eliminate the simplest thing first. Assuming that everything is intact and as it should be, the one basic thing worth checking is the state of the metal faces that the head stock swivels on. You will need to disassemble the whole thing. head stock, motor and all to check it. It's VERY HEAVY! You do this by by taking off the bolt.
Basically, what you are looking for is the couple of drops of oil that you put into the front bearing eventually travels through the bearing and has to go somewhere. It may, in time, migrate through to the base plate bolt hole and lubricate the swivel point that you're trying to lock off. It has been known to happen over years of use. It shouldn't happen, but too much oil sometimes goes in and cleaning inside the head stock can be forgotten!
Essentially, the contact faces where the head stock swivels on the base plate should be clean dry metal and have a reasonable degree of friction. A wipe with some emery may help.
Good luck.
