Are we really talking about lube?
I used to work on tape decks. My dad did too so I know what he advised as well.
The proper answer is fine machine oil. If gun oil (lubricant) is a light, fine lubricant it ought to work just fine. One outfit I worked for was so cheap they wouldn't spring for the good stuff so they'd use 3 in 1 right off the hardware store shelf. That'd make my dad cringe. The 3 in 1 was adequate for most applications. Lots of motors had sleeve bearings. The motors had plenty of torque, it worked fine. You wouldn't want to use that stuff (3 in 1) in a critical application like a phono tone arm. You really want to hold out for a light, high quality oil for something like that.
The problem with any kind of grease is that unless you can get into the bearing by disassembling the whole part it is unlikely you'll get the grease where it needs to be. On the other side, more than a person or two has squirted WD40 all over everything. WD40 can do awful things to previously applied lubricants making a gummy mess. It isn't a friend of rubber parts either. Ya hear that? We're talking lube and now we've turned the conversation to rubber parts.
Less is probably better which is why many electronics stores used to ( I haven't looked lately) sell small precision oilers with a clear plastic vials about 1/2 an inch in diameter and 4 or 5 inches long. They had a precision hypodermic [type] needle.
Inasmuch as you already stuck the gunk in there it don't make too much difference now. Just be sure not to over oil or the lubricant will get on the rubber parts. Thats a sure ticket to the junk yard as parts can't be easy to come by.
You didn't say what the machine sounded like after you lubricated the capstan bearing. If it has been allowed to run dry for a lengthy period, it will have excessive runout. The lubricant can only help if it was running dry. Man, you don't want to run dry. Do ya Hilda?
Hope that helps.
