Okay, someone said they'd like me to infodump more advanced paper repair techniques, so I'll give the people what they want. I don't have pictures of my own ATM but I'll link a video at the end.
Disclaimer: you are not a professional art conserver (unless you are) so don't try anything here on art that isn't your own and you own the consequences of your actions. I'm explaining these techniques for personal use fixing your own mistakes, not repairing fine art for museums. Not responsible for bad outcomes. Practice this shit before using it on something important.
The main trick is, you want to use torn edges on the original and the patch instead of cut edges when possible. Since the subject here is making corrections to your own art, you have the luxury of creating your own edges and don't have to work with what you've got with art conservation. Torn edges blend together and the fibers overlap, which creates a bond that is both stronger and less visible.
Creating a precise, controlled tear is the trick. In thin paper you can just do this carefully with your fingers. On thicker paper, you'll have to use assistance to get it done.
Use a small brush and clean water (or if you've got it, reloadable soft tip pen that you have loaded with water) to trace the outline of where you want to make the tear. Then, try pulling it apart. You want to keep the paper as flat as you can and pull the edges directly away from each other to leave lots of loose fibers.
If this doesn't work (very tough paper) you can instead use a sharp needle to tear it. Manually perforate along where you want the tear, then use the needle dragging sideways (perpendicular to the tear) to pull the edges apart little by little. As always, the goal is an edge with lots of loose fibers.
To make a patch/fill that's the same shape as the hole, lay a sheet of plastic or mylar over the original to protect it, then place your fill paper over that and trace the outline of the shape you need. A lightbox is very helpful here, or hold things against a window if they are small enough to manage. Use the same tearing technique to create a patch with fuzzy edges (I'm assuming, since this is your own art, you have more of the original paper to make the fill and don't need to find or make something that matches).
To attach the patch, you want to use paste. Either old-fashioned starch paste, or methylcellulose. There are lots of tutorials online how to make this so I won't go into it here. Starch paste won't hurt the paper, and you can unglue it using plain water if you need to make corrections. You absolutely don't want to use self-adhesive tape of any description, which can't be removed and guaranteed will damage the paper over time.
Apply paste to the torn edges of the fill with a brush, by placing it on a flat nonporous surface like plastic or glass, brushing outwards to draw out the fibers. Then peel it up and put the fill in place on the backside of the art (tweezers may help). Use a brush to smooth the loose fibers outwards and bridge the join. A bone/teflon folder is also helpful to smooth things down.
Place a sheet of spun nonwoven nylon cloth over the fill (brand names Reemay, Hollytex), then some scrap blotter paper, and finally a flat weight. Let the paste dry under weight so it stays flat. Regular nylon or other synthetic fabric might also work, but I never tried it.
If necessary, reinforce the join with torn straps of Japanese tissue paper. This may especially be necessary if your paper was very short-fibered to begin with and couldn't make a lot of overlap. Ideally You want the expensive handmade stuff made of kozo or gampi, as thin as you can get it (I'm talking 5 gsm tops). It's quite pricy but a little goes a long way. Attach strips along the edges using the techniques above. With the really thin stuff you can apply it to the front as well, it's so thin you can see through it once glued down. You can also do this to repair simple tears.
Videos of these sorts of techniques in action: