Have no fear of looking through the eyepiece. You are not looking through the lens. Keep that in mind, cuz you should not trust any focus set in advance. If you have access to a sturdy old long tele from the preAF days thaz a lens that holds focus. Modern lenses use so many delicate moving parts that you cannot trust them to not shift a bit in transit or when being handled. Carefully focus that lens in magnified MF after framing your subject. On a tripod you could also use the horizon as a substitute for infinity focus distance. The extra 93,000,000 miles wont matter. No infinity can be larger or longer than any other infinity. IIRC infinity focus is anything beyond 1,000 FLs ... about 600 yards for that lens. For a solar eclipse, your foreground object is about 440,000,000 yards away.

When you say "nothing in Manual mode", do you mean you can't press the shutter or the picture is blank? If the later, you might check the settings, shutter speed, F stop, etc. And again I assume when you say manual, the auto focus is still on? If not, turn on auto focus first and put the camera in Manual mode which should still allow auto focus and see if you can take a picture first before switching to manual focus.

If using a tripod, you can turn the VC off. The MF (manual focus) should only be turned on after you can take a picture in Manual mode by setting the correct shutter speed and F stop.

Welders glass has to stop UV rays. Otherwise welders would be blind. Welding generates strong UV with the high energy electric welding. I did welding for a while and learned about people who did not heed warnings about welding without using welders glass. The UV is a part of the very bright light produced by electric welding. And during the film days, the welding glass was what I used on my telephoto lens for a total eclipse. I viewed the stages up to totality through the telephoto lens with no damage to my eye. When I was younger and ignorant of the facts, I tried using multiple fully developed film and came within less than a second of losing my eye. After that very, very close call, I educated myself about things that could damage my eye and prevent me from doing photography. I promise you, I would not recommend welders glass unless it would be safe for use.

And, yes, Thousand Oaks Optical is a supplier for solar shades. I have used them before and found them to be very reputable.

Two more thoughts. (1) If you can find solar shades on line, you might be able to get them in time (check the NASA site). (2) If not, consider going to a welders supply store and see if you can get an 18 ND or 19 ND welders glass. You can test them in the parking lot for what you like better. I have the 18 ND in a size that I could mount on my film camera's telephoto. Now I have used it several times since for just simple viewing since I have a photographic filter for my mirrorless camera. The welder's glass will stop UV rays from reaching your retina and burning it. The polymer shades will do the same (can be worn while the welder's glass has to be held). You can view for hours with no danger. I cannot say that about a photographic filter.