Hi Jarno,
First off, welcome!
The good news, you have most of the lights working and you have done some good troubleshooting.
Here are some thoughts to what you are seeing and some things to look at further.
You stated this.
Original wiring and all wires work except the running light. I have continuity from the green wire (running light) to white (common ground), removed all bulbs, and measure around 50 Ohms.
First part, with the light bulbs in, yes you will get continuity between green (hot for running light) and white (ground) due to the bulb filament making the connection.
When you pulled the bulb and found 50 ohms, here we need to confirm how you did the 50 ohm test. With the bulbs out;
1. Was the 50 ohms from the green wire to the white wire?
2. Was the 50 ohms from the white wire to a separate known good solid ground? (like the 7wire cable for the truck)
3. Was the 50 ohms from the green wire to a separate known good solid ground? (like the 7wire cable for the truck)
Need to confirm this before starting to speculate where the 50 ohms is coming from.
Using a jump starter as 12V source, I get all lights to work, except running lights. When using the jump starter with the green and white cable, voltage immediately drop to 9V at the jump starter, and I'm measuring between 2-4V at the tail lights. Somehow I think the green wire is shorted to ground, but 50 Ohms is kinda high for a short?
Question, were the light bulbs in or removed when you get the voltage drop down to 9V? This is a key piece of info.
It does appear you have an issue with the green hot wire crossed to ground, somewhere in the camper. The voltage drops points a high current being pulled when the green is hooked up.
I am not totally sure on a 86 Sunline, but I am going to speculate on how the wires where run as being close to the newer Sunlines. On the newer camper, the front wall and left front and right front amber clearance lights (front running lights) had a green and white wire junction at the 7 wire cable tie in and ran up the front or side wall, then jumped to each of the 4 amber lights. They parallel daisy changed them together.
The rear wall, rear left and rear right red clearance lights green and white wires were separate from the front. A long green and white wire ran under the camper from the front 7 wire junction to the back wall, then up inside the back wall and daisy chained tied all the red clearance and tail lights bulbs together.
BUT, there always seems to be one, on the older campers and the 86 could be in that group, Sunline use to put glass fuses in the DOT lighting circuit. Look to see if your camper has that glass fuse set. Most times, it is near the power converter and AC breakers. If they did the glass fuses, then that fuse set may be where the green hot wires start from and not up front at the 7 wire cable like I talked about above. The 7 wire cable green could go to the fuse set first, then through the fuses, then out to the lights. They may have run a green hot to the back wall and a separate green to the front wall starting at the fuse set.
You can try this to help sort out where the issue is occurring. Take out all running light bulbs. This testing also is all going on the assumption, your 50 ohms was from the green wire to white wires with no bulbs in place.
First, if your camper has the glass fuses in the DOT lighting circuit, see if there are any crossed connections, (stray wires) from the green to the white.
Second, still at the fuse set, put you ohm meter on the green wire to white wire with the fuse in to see if you get the 50 ohms. Ideally you get the 50 ohms. Then pull the fuse. Now there is a break in the green wire from the 7 wire plug to the camper lights. See if the camper side is where the 50 ohm is or on the 7 wire truck plug? If it shows that the 7 wire plug has 50 ohms and the camper shows no ohms, then you know the issue is between the fuse block and the 7 wire plug. If there is a replacement 7 wire plug on the end where the end comes apart, pull that plug apart. There may be a wire strand between ground and the green as there are screw terminals in there. A wire hair can cross over.
Last, you might try this one at a time with this test and then eventually will have all lights out. Again, all running light bulbs are to be removed. Take your pick on where to start, but pull the first running light out of the wall to expose the wire nuts on the white and green wire. Unhook the green wires at that light. Separate the green wires, test for ohms between greens and white. Odds are there are 2 green wires on most all lights. if you only have 1 green wire then that is the end of the daisy chain run. What you are looking for is where does the 50 ohms drop out from white to green?
NOTE: when you unhook a light, and there are 2 green wires, one side my be 0 ohms and the other wire 50 ohm. That helps tell you the down stream lights from that joint are OK and the problem is on the other wire. You can then test which lights upstream or down stream are OK and which still have the 50 ohms. You can leave the first light green wires unhooked, then go the next know problem light that still has the 50 ohms and pull it apart. Test each side. You keep going this until you find where green wire has the 50 ohms to ground and the rest are OK. Once you trace that down, then you have to figure out how to replace that wire or find the short in it. Some where there could be a skinned or chewed green wire with a corroded connection to the ground wire or the metal siding or trailer frame.
Hope this helps and let us know how it goes.
John