Jtdcftul

(Please see edit below; problem might actually be with brake lever)

I'd like to know if a temporary resolution is possible for my stuck rear brake cable.

Video:
https://drive.google.com/file/d/1EmGB78BphkK4k27j4BNouMpIK31A31ST/view?usp=sharing

I'm taking it into the shop but the soonest they can take my bike is Tuesday. I have no experience in bicycle repair. The bike is only half a year old, but I've been riding it in winter. I clean the brakes (excluding the pads) every one or two weeks with a soft bottle brush and diluted dish soap. I have never lubricated any brake parts yet, though.

Edit: I might have been wrong on the location of the malfunction. The brake lever seemed stuck, and I assumed that was because the brake was stuck, but after squeezing it very hard it seems to work to some extent. It makes a creaking noise and doesn't move as freely or with as much range as the front brake.

From the video, it looks like the cable has frayed inside the outer housing or something like that. I doubt there's anything you can do except get the bike shop to replace the cable.

Although most of the braking comes from the front brake, I woudln't recommend riding the bike in this state: you'd have no back-up if anything went wrong with the front brake.

In addition, that cable looks dirty to me in the picture and video. Maybe it's just the lighting? But if you have anything like WD-40, you can spray it on the cable and see if it loosens up. It's worth trying as it won't hurt anything.

If water gets into the cable housing when you're cleaning the bike, something like this could happen as the insides of the cable might rust up.

Looks like excessive friction between cable and cable housing. Probably caused by a frayed cable or a kink in the housing. Is the cable housing damaged somewhere?

I’d try unclamping the cable at the brake and then check if the brake moves freely. You can then also unhook the cable at the brake lever and check if it moves freely as well. This would prove that the cable (or its housing) is the culprit. Light, penetrating oil (e.g. WD-40) could temporarily help to get it moving again, but if it’s damaged it could fail completely at any moment.

You could replace the cable yourself, it’s quite easy. Replacing the housing is a bit harder and works best with special tools but if you are only replacing it you already know where it should go and how long it has to be.

Riding without a rear brake is relatively safe (as long as the front brake works properly). Just make sure you remember that you don’t have a working rear brake, especially when indicating a left turn (assuming your rear brake is on your right hand).

As others have said, looks like rust/corrosion increasing friction.

To repair teporarily You could try dripping some solvent and lubricant onto the inner cable so it weeps up into the outer. This might get it moving slightly better, but is not really a fix.

To Repair PROPERLY: replace the inner cable completely, and depending on the condition the outer sheathe too. This is not too hard and can be done by the home mechanic.

You'll need a replacement inner cable with the right mushroom head. Look inside your brake lever to see what the end looks like. I'd be 99% sure its a MTB or off-road design, which is a cylinder shape with the wire coming out the curved side (right in image). The road one is a double cylinder with the wire coming out the centerline vertically. (left in image)

You simply undo the retaining bolt/nut at the brake, feed the wire out, undo from brake lever, and then Haynes it back in.

If the new cable is hard to get through the old outer, you might have corrosion or wear in there too.

A kit with enough to do a whole bike is less then the cost of lunch, and will contain two inners and enough housing to do the lot. Example:

As for tools a cable cutter would be nice, but not required. Trimming the excess inner can be hard - check the answer at How to cut a brake/derailleur cable? for tips and techniques there.

Prevention I can't see in your video or image, but rust is caused by water and aggravated by salt. So keep your bike dry and wash off any road salt after wet rides. Also helps if your bike is stored in the warm and dry overnight. Outside in the rain will certainly accelerate rust.

It is possible your rear brake is poorly routed too. If the lowest point is not an end then water will pool inside the cable. If this is the case consider rerouting the cable on the frame, perhaps up the chainstay. You can also use longer lengths of outer housing and skip some of the frame stops. Water can't get through the outer housing, it only goes in the ends.

Another thought is to protect the end of the cable better. You could possibly put a squirt of marine grease up the outer before fitting the inner. This should provide some level of seal to reduce water ingress, but it reduces water egress too.

Last thought, a V brake noodle-boot may provide additional coverage if threadded over the inner, where it exits the outer down by the caliper. I'm talking about the black rubbery bit here - (its only half the cost of lunch)

All this is within reach of the home spanner wielder. Any questions do ask here or check in [chat]