There are few things you can do. One of the bigger issues is if you want the manuscripts to be able to be rolled. If you are willing to keep them flat, you can fairly easily gild.
As you've already noted, a red background shows off the gold. You could also use a dark yellow ground. I haven't use egg tempura, but you may improve your chances by burnishing it a bit before adding some adhesive, to reduce the chance of it not sticking. Do either base colour and then a thin layer of rabbit/animal hide glue and then the metal foil. You do have to get the timing right with the natural glues. You want it juuuust almost fully dry, but not quite.
That is the big benefit of the modern stuff. It has almost no limit to its working time, so long as it is clean.
You could also try inks instead of the tempura, just on where you want the gilt.
Gold prices are super high. I've barely ever worked with actual gold. Most of what you can get is brass. It looks good but can tarnish over time if it's not sealed. It's been 10+ years since I did any buying so things may have changed but the Japanese stuff was hugely better than the German, which were the 2 main types out there. I always worked with loose sheets in books of usually 10 to 12 pieces rather than the stuff mounted to paper that you peel off.
You can cut or break off small pieces that are just a bit bigger that the area you want, use a static charged clean and dry paint brush to move the scrap over and another soft clean brush to smooth it down. It will crumble and brush away where there isn't any glue.