On some sets getting to the pilot light(s) can be difficult.
There are 3 solutions to this, besides trying to get your fingers on them.
One is to use a piece of heat shrink tubing the correct diameter to slide over the bulb and remove it.
Two is to use a piece of rubber tubing that fits over the bulb and use that. (Best solution I found, barring having the actual tool).
Three is to use an actual pilot light removal tool. (Yes, they did really make these).
That being said, I have seen lights that got so hot that the contact on the base of the bulb actually soldered or "welded" itself to the contact in the socket. They can be a pain to get out without damaging the socket, or the glass breaking & cutting your fingers. So use a bit of a shop towel to prevent this. Personally, I believe this was caused primarily by the spring getting weak, and causing higher current flow thru the contact button or arcing which melted the solder & caused the two to be resistance soldered "welded" together.
Also you will find times that the really old pilot lights used natural rubber insulation, and the insulation crumbles away, leaving the wires to short to each other.
On many occasions I have been able to disassemble the socket and solder a new piece of wire to the bottom & side contacts of the socket.
Sometimes, they put a "dimple" in the base of the socket to prevent the little Bakelite disk & spring from popping out when the bulb is removed, and sometimes not. You can smooth out the dimple with a piece of rod and a hammer enough to get the socket apart, then carefully, "re-dimple" it with a screwdriver or punch & hammer. It does take a bit of skill and patience.
I make it a practice to save all pilot light sockets from junked equipment. New ones are really not obtainable in the configuration you tend to need. (Sort of like having every bolt but the one you really need).
I have salvaged the disk contact and the springs out of them more than once to rebuild a damaged socket. Sometimes though, you have to get creative.
Some of the old inline fuse holders used a similar method of fuse contact, and I have used the contacts out of them to repair sockets with. It does take time to grind it to the correct size and modify it, but it can be done with enough patience and "Blue Funk" floating in the air.