Go here and have a look.

https://pinside.com/pinball/forum/topic/firepower-tech-repair-and-restore#post-2276297

There is another thread that I found similar information about the warming resistor but I can't locate it at the moment. My LED flashers worked once I cut out the warming resistor. Just make sure you clip the correct one...

Heat up the leads on the old one, remove it, replace it with the new one. Just solder it in there. If I recall correctly, it doesn't matter which way you put it in as they don't have a polarity. If you want to be sure, match up the direction of the bands when you put the new one in.

What happens when you turn the game on? In "attract" mode the 89s will flash at the same time. You can also put the game in diagnostic mode and go into the solenoid test. When you advance to test 15 the 89s will flash continuously. When you say you push on the socket and the bulbs come on, do they both come on or just one? To me that sounds like a bad socket or a loose wire. The bulbs are in a series and if one doesn't work, the other won't either.

Sockets aren't expensive so I'd look at replacing them as the first step. It's a bit odd that they both don't come on when you push the blue one in. I realize someone said it doesn't matter which way you put the bulbs in but try pulling the blue one out, rotate it 180 degrees and put it back in.

When are you actually pushing on the blue bulb, when the game is in attract mode or in diagnostic mode? Other than during gameplay, that's the only time they should come on.

Okay, that's not normal behaviour in attract mode. The 44s will flash and then the 89s will flash. The 89s never stay on. Watch the beginning of this video -

If the 89s are staying lit that means there's current flowing to them. Are you sure that resistor isn't toast? Take a picture of the board and post it. When you start a game, if you push on the blue 89 will the red 89 come on as it does in attract mode?

You might as well just snip off the half of that resistor that's still on the board. It won't make a difference but it looks horrible sitting there like that. Check the path of all the wires between the two 89s and the board. Check all the other wires soldered to the board. Make sure everything is solidly connected. If a wire came loose or popped off, solder it back on and make sure it stays.

I'm going to go have a look at mine and get a picture of my board and compare.

The other thing you might want to do is swap the bulbs to make sure that they both work. Do the same thing you did before to get the red one to light up. I know this sounds stupid and the bulbs are probably brand new but you want to make sure that something really obvious isn't causing more problems.