I had an identical problen that turned out to be the wiring at the connection to the headlight. I had put in all new wiring but connected the headlight socket incorrectly by switching the positions of the yellow and brown wires at the connector. Switching those wires back solved the problem.
Assuming you hadn't taken everything apart and put it back together wrong like I did means your problem is (1) bad bulbs, (2) bad fuses, (3) bad relay, (4) bad signal switch or (5) bad wiring.
A clue here is that your high beam indicator light doesn't come on. As it is powered directly from the high beam circuit at the fuse block, this seems to point out that power isn't coming off the fused side of the system.
The first obvious check is the fuses. I've had fuses that looked good still test open. Pull them, clean the contacts on the fuse block and on the fuses themselves and, after testing them with a continuity tester, replace them.
If this doesn't help, go under the hood, behind the dash and identify the wiring at the fuse block that you're concerned with. On the bottom side of the fuse block you'll see two white wires, one of them doubled with a blue wire with a white stripe. These are the wires going to the high beams (the blue/white iwre goes to the high beam indicator.) The wire at the top side, opposite the white wires, goes to the high beam relay. Make sure it is secure on the connector. You might want to pull it off and ise emory paper to clean the contact. Trace it back to the relay which should be clipped to the dash support above the steering collumn. Check the connection at the relay like you did at the fuse block.
If the problem is still there, it's most likely either the relay or the high beam switch. You can check the switch by going to the relay, pulling the wire that is brown with a white stripe. This is the switch wire. Use a continuity checker between it and ground to see if you get an indication when the switch is pressed. If you do, the switch is good and the remaining culprit is the relay itself. You might try using a small variable force applicator (hammer) against the relay. If the contacts are stuck this might jar them loose.
Or you can save yourself a lot of time and bother and just replace the relay, as it is most often the problem and is easiest to get to to fix.
'66 sunroof Beetle