A few items of interest and importance here. One, so many DIY types think that all motor homes and lighting systems are the same, not so.
Just because someone want's to change an item on any part of their coach, is no reason to show disapproval. Lighting systems, especially rear tail lighting systems, start to fail in many ways over time. That includes not only the wiring to them, (get's corroded, dirty, rusty, etc. at the connections and bulb insertion points) but also, the tail light lens's, like many items in and on something that sees UV for most of its life, will begin to fade and or become at the least, opaque. LEDs, do draw considerably less power. But, for about 99.999% of the application in tail, marker, head lights, clearance lights, brake lights, turn signals, and just about any EXTERIOR light, the need for less draw on the electrical system has barely any value. It's nice, but not needed.
What is of more importance is, in many cases, today's LED light bulbs can, and often do, display a brighter array of light, than the ones they're replacing. Much of that is dependent on the chip set the light bulb or, entire light assembly is made with. There's cheap LEDs and, expensive ones. And, contrary to popular belief, LEDs in many cases, DO NOT last forever. I've been dealing with LED tail, marker, clearance lights for years. I've seen very expensive LED tail light assemblies, with only 3 years on them, have almost half the segments burnt out. And, I've seen that many, many times. They are not as "long lasting" as some think.
In a situation like the OP is presenting, maybe a question or two should be asked before making any real suggestions as to a path of improvement.
1. Are the OPs tail lights the type of tail light in which just the bulb can be replaced.
2. If they are that type, what are the condition of the lenses, clear, opaque, faded, burnt (seen that a few times from incandescent bulbs developing heat and being too close to the lens) etc.?
Finally, the "Safety" thing is of great importance here. The "Sun at your back" is a great example of how to look at this situation. When the sun is directly on a set of tail lights, depending on the actual lights, they can be almost impossible to see, what the driver is indicating in intentions.
A bright acting, highly visible tail light, brake light and or turn signal, in direct sun light, is ultra appreciated by following drivers.
And finally, the "blinker thingy" is simply a relay or, "flasher" that has what's called a Bi-metal spring in it. When a turn signal is applied, 12V is flowed through that flasher. The load, as in the filament in the tail light, is directly in line, with that bi-metal spring. Due to that load, the bi-metal spring heats up and, springs away from it's contact point. At that time, you have no light. But, that bi-metal spring, cools off and, re-contacts it's contact. You have light. It does this at the frequency we've all seen over the years.
But, when an LED is introduced into the system, because LEDs require waaaaaay less electricity to operate and therefore, produce less draw, the bi-metal spring get's confused. In some cases, you'll not have any blinking at all and, in some, it will blink real fast. And, in the case of later electronics in later coaches, it's possible that the owner will see a "Bulb-out" signal on the dash, due to the fact that, the system is used to incandescent bulbs and a certain load being read. But, when the load is severely reduced, as in when an LED tail light bulb is inserted, the load is no longer there and, the system sees that as a fault and, will display it on the dash.
These are just some of the considerations when thinking about changing to LED bulbs. The older the coach, the less potential problems will arise when changing to LEDs.
Scott