I have always considered the front markers to be parking lights, but calling them running lights is perfectly fine and I would consider them one and the same. The OP is perfectly fine not using these lights in the USA. Capping them and only using the turn signal wires is perfectly legal.
"Parking lights" are lights that you turn on so that drivers can see your parked car and not run into it. "Marker lights" or "running lights" are lights intended to make your vehicle more visible on the road. There is a big difference between these concepts.
And I think you will find that you are required to retain all lighting functions that the vehicle had originally. You may get away with not having the marker lights because some makes/models didn't have them and no cop could be expected to know which ones did but, why would anyone want to make their bike less safe by making it harder for other road users to tell what it is at night? Or give someone in a car an excuse to run into you and claim that they couldn't tell what your bike was or where it was on the road).
Not to mention that their lawyer could bring an expert to court to show that the bike didn't have the marker lights it came with and put the blame on you.
FWIW, I have turn signals that do not act as marker lights on both of my bikes but I also have separate marker lights.
'82: 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).
The best advice anyone can give you about customizing any vehicle is to get it safe & reliable in more or less original condition and use it for a while before you start making any changes so it can tell you what changes it needs to make it do what you want/need better. That approach almost always results in something you actually want to keep and use but making changes based on style or on what someone else (who may or may not really understand how the changes affect the way it works) has done often results in a piece of expensive yard art that you can't stand sitting on for more than a few minutes and might even be dangerous.