Your Speedometer cable does not hook into the engine. The speedo cable screws into the speedo drive in the left side of front hub.
The tachometer cable hooks into the engine. When unhooking the tach cable the adapter may unscrew with it.
There is a part #1 in the pic that is held into the case with a set screw. An adapter, #4, threads into part #1. The cable housing threads onto this adapter #4. Often the adapter unscrews from part #1 instead of the housing off of #4.
Any way once you get either housing unscrewed you can remove the inner core. Clean it up. This core is twisted wire. It can rust inside the twisted wires, swelling the core. This can cause binding. If the core is rusty the housing will be rusty in the same area. If bad enough you may have to replace it.
If just dirty clean the core and a thin coat of grease. I like the Super Lube that Harbor Freight sells. It all synthetic grease. Leave about 3-4 inches on the end that goes into the gauge clear of grease, If done clear to the end some my migrate into the gauge and mess it up.
To clean the housing I use spray carb cleaner, brake cleaner or some such. With both ends unhooked spray some cleaner into the top of the housing till it runs out the bottom. Let set for awhile then spray more. Repeat as need to the stuff running out the bottom is clean. I then use an airhose the blow through the housing to force even more crud out and dry it.
Now when you install the greased core back in it shouldn't squeak.
Leo