An easier way to test is just to check the resistance across the EOS switch. Power off, meter set to ohms, one lead to each EOS connector (wire). If more than half an ohm, you need to either clean the contacts (400 grit sandpaper works) or you need to increase tension on the contacts.

Many new high power EOS switches come with a protective coating on the contacts. Best to check for this with the meter before installing. As mentioned above, 400 grit sandpaper will remove the coating. Occasionally the leafs won't be tensioned properly. Practically no resistance when you hold the contacts together, lots of resistance with no added tension. Use needlenose pliers or a switch tool to slightly bend one leaf to add tension. Get it under half an ohm outside the games, then install it.

For future reference. You should be able to get yours going in the game.

Cosmic Gunfight and Blackout do use the same rebuild kit, but I don't recommend buying rebuild kits on eBay. Flippers are the most important mechanisms in a pinball machine. If you're going to skimp, don't skimp on the flippers.

Looking at the pics, the plungers are too short.

Use sandpaper to clean the outer switch on the lower right flipper. That switch provides power to the upper flipper. New high power switches (big contacts) can often be oxidized, causing resistance. Can't see the oxidation, but if you measure resistance across the closed contacts, you can measure it. Should be less than 1 ohm resistance. If more than 1 ohm, sand until it's under 1 ohm. 400 or 600 grit works fine on new switches.

Also make sure the switch contacts are meeting evenly when closed. Contacts look a little off in pics, but may be ok once switch is closed.

Very common for the EOS bracket to break on Stern's, so yeah, hang on to the old parts.

Stern links often wear where the bushing goes. Can't see the wear looking at it, but can feel the excessive play caused by the wear by wiggling the parts back and forth. Once disassembled, you can see the wear in the link hole.