The glow plug controller turns on the glow plugs for 5-15 seconds to warm them, then cycles them to keep them warm. On - Then on, off, on, off, till you start the engine to keep them warm. (If working correctly.) Your light is dimming because glow plugs do take some good amperage to run and drop the vehicles voltage, thus the lights dim. (But should be minimal dimming.) If the dimming is severe you may have a ground issue as you mentioned you put in two new batteries so the glow plugs should only be changing the voltage a volt or two.
You show 2 very burnt wires from what I take is your headlight switch. So for wires to burn up like that you must have a positive short to ground that the fuse could not over come. Now you have wires touching so fuses blow as wires not intended to touch each other or touch metal objects cause the fuse to melt. Perhaps someone has tapped into your light circuit to power something high amperage. Perhpas the wiring for the box truck is causing this. Also look to the trailer wiring if you have that as well. But likely you have a short to ground. Keep in mind those wires likely burnt the covering of other wires and now likely touch, or will let them touch something else. When they do, it will blow the fuse.
Suggestions -
Wiring issue -
1) Get a wiring diagram but know the cargo box wiring may or may not be Ford OEM. So you will have to manually chase that part.
2) Replace those burned wires with new ones. Get rid of the wire nuts someone installed, those are for 110v wiring, not for vehicles.
3) Chase those burned wires back to see what else they burned and repair those wires too. Replace the melted ones, tape up collateral ones if minimal damage, or use liquid tape is only minor damage.
4) Remove, clean, and re-install all the grounds. From battery to battery, battery to engine block, from block to frame, block to firewall, etc. Also the battery wires on these trucks corrode and go bad (Usually they swell and spit the plastic and have a lot of white corrosion.), so if they are marginal you may want to replace. You may have a bad ground situation, but have not seen that cook wires like yours are. Usually it causes lights to dim, not burn wires.
5) There also seems to be a fair amount of corrosion on your fuse panel. You may want to watch for leaks from the windshield, vents, firewall, etc. If you live in a humid place perhaps this is normal, but if not it would appear water at times has been dripping down your fuse panel.
Power issue -
Know that many of these trucks where geared low and 65mph is pushing 2,800 RPM. However empty you should be able to go 65mph. You also are pulling a big wind sail around with that box so it will slow you down some at higher speeds. But still you should be able to do 65mph. Most of these are former U-haul trucks so hard to say if yours was. But if so hard to know miliage or what was done at each U-haul maintenace yard this pulled into over the years.
Suggestions -
1) See if it happens on both tanks. (Not sure if your van/box truck has 2 tanks like a pickup, but if it does make sure both tanks have the issue.) The pick up socks are known for going bad and clogging. If the truck appears to starves for fuel it will run oddly till it gets enough fuel again.
2) Set the timing on your injector pump. Many mechanics lack the tool to do this, so they do it by ear, which is not very accurate. Also changing injectors will change the timing. Its all mechanical, so if last timed with worn injectors they would have changed the timing. Also not all injectors are created equal or have the same PSI opening pressure.
3) It has been discussed some trucks were governered down via the injection pump. So look to that as something that could have been done. Perhaps U-haul or some other truck vendor for safety reasons tuned the pump down to prevent folks from speeding and getting hurt or hurting the truck. You will feel the truck stop accelerating and perhaps slow up till you are below governed fuel level, then start to accelerate again. There was a recent post on this you can search for. My truck for reference can do 3,300 RPM's I never go there but the IP does not limit me from doing so.
4) Due to the unknown miliage if after setting the timing and checking for a govenor change, you should do a compression test. There is not PSI suggestions rather that all are within 20% of each other. But if you have less than 300 PSI I would imagine that is part of your challenge. My truck for a reference is about 410 PSI accross the board with 5 compression strokes during the test.
5) If you are comfortable your fuel system is good, you do not have air intrusion in the fuel system, your timing is good, and your compression is good. It's time to send the injection pump (IP) out for testing and possible rebuild. Then you know it is not governed and is putting out the desired pressure and volume. Be sure to re-time the engine when you put the injection pump back in.
Stay the course, just know you are not alone, you are not the first person to get a neglected IDI truck, have to do some work to get it running right, overcome mulitple issues the prior owner avoided, and spend many hours doing research. Keep in mind a new diesel truck is now over 65K without the box, that these are some of the easiest diesels to work on, parts are cheap, and information is very easy to get off the internet and in groups like this. Once you get it running as you wish it will serve your well.