Have you checked the main fuse (located under a cover on the side of the solenoid)? Those so-called "dogbone"(open link) fuses deteriorate over time and can develop cracks that can open depending on the temperature or engine vibration (I've even heard of a few that disintegrated when touched). The common advice here is to replace the original fuse with a modern blade type fuse in an inline fuse holder
Your brake light is on the same fuse as the turn signals and horn but the tail light is on a different fuse (should be the same one as the marker lights in the front turn signals and the lights in the instrument panel) so if both the tail and brake lights (separate filaments in the same bulb) go out the problem could be a bad ground (green wire) connection where the light plugs into the bike's main wiring harness under the seat.
Welcome to the forum. Please add your location and your bike's model and model year to your profile so that you don't have to remember to tell us every time and we don't have to keep asking when you forget (see Forum Settings link in my signature).
And welcome to the world of antique vehicle ownership (they own us, not the other way around). Your bike is about 4 decades old and may or may not have had all of the maintenance necessary to keep it safe & reliable so it is highly recommended to download the Factory Shop Manual for your model (available through the CX Wiki - link in my signature) and go through all of the service procedures, regardless of whether your bike has reached the specified mileage.
I also recommend looking on all rubber parts with suspicion because rubber does not age gracefully. Check the date codes on your tires and replace them if they are over 5 years old no matter how good they look & feel (old rubber simply cannot flow around the irregularities in the asphalt well enough to grip, especially if it is cool or wet). If your bike still has the original rubber brake line(s) (should be replaced every 2 or 3 fluid changes = 5 or 6 years) I recommend shopping for modern stainless braided ones (they last practically forever and double the life of the fluid). And don't forget things like the rad hoses and the boot between the engine and swingarm (they can crack on the bottom where you don't see it).