I tend to like my games with the tilt not working

It's a capacitor. It should not show continuity.
Without this capacitor installed the tilt mechanism should still work. It just won't be as sensitive.
If you push and hold the tilt plumb bob against the outer ring and tilt isn't recognised, you've got some other problem (probably connector or wiring).

FYI, this is a replacement capacitor (0.047uF 50V):
https://www.greatplainselectronics.com/proddetail.asp?prod=CCD-0.047uF-50V

You need a capacitor/ESR meter to test it properly. Having said that when these capacitors fail they typically become resistive/short circuit.

So put your multimeter on high resistance ohms Ω mode and measure across the capacitor out of circuit. Your meter should indicate the capacitor as being open circuit. If you measure constant resistance across the capacitor it's likely internally shorted and bad. Make sure your fingers aren't touching the metal tips of the meter probes otherwise you'll measure resistance through your body and get false readings.

The playfield will also have these capacitors on switches that need to be sensed on fast closures. These capacitors (usually the green colored ones Bally used) do fail and go short circuit causing multiple problems with switches.

So the game still isn't tilting when you manually activate the plumb bob tilt? Do you have both tilt wires connected to each part of the tilt mechanism?
What about when you close the tilt switch on the bottom of the playfield? It's usually located near the flipper mechanisms.

Your Paragon will be set up the same and you can use it for reference.

Post a picture of the wiring to the tilt plumb bob if you don't have any luck fixing it.
There should be a wire connected to the ring, and another wire connecting to the upper wire shaft of the plumb bob.

Thanks for the pictures, that helps.
If you look at the end of the tilt roll cage where you have the two red-yellow wires and the white-black wire, Paragon shows there is a diode connected between these wire sets. However your Flash Gordon is missing that diode. Essentially that white black wire going to the plumb bob is not connected to the circuit.
Install a diode with the banded side of the diode on the white-black lug on the cage switch.

Get some 1N4007 diodes. They're very common diodes and are also used on solenoid coils.

I have literally hundreds of these. Swing by after work and I can give you some.

The manual (pg 47 of the IPDB .pdf) calls for 1N4148 diodes on all switches, the 1N4004 are for the coils. Pinball Resource does list the 1N4148:
XO261 DIODE 1N4148 GTB-XO261 $0.50ea

Quy, I dont have any of those. I have the standard IN4004.

Anyone know what the difference is?

may not work?

"The 1N4004 is designed as a rectifier diode with a 400volt 1 amp rating.
The 1N4148 is a high speed signal diode rated at 100volt 200ma."

Without looking at the data sheet I'd guess the 4004 will handle much higher voltage without dying. It might still have low enough forward bias to work even in the switch matrix. Maybe G-P-E or Quench knows for sure.

also this thread suggests it may be fine?

https://pinside.com/pinball/forum/topic/difference-between-1n4148-and-1n4004

any experts able to teach us here???

order 10 extra for me please. Assuming these are needed, it is nice to have spares

There is a note in the Pinwiki: http://www.pinwiki.com/wiki/index.php?title=Bally/Stern#The_Importance_of_Diodes_and_Capacitors_on_Switches
"Bally and Stern both state 1N4004s as original, but 1N4148 diodes can be used, and in some cases, were used from the factory."

Bally switched from using 1N4004 on their switches to 1N4148 sometime in '79 or '80
1N4148 are faster switching diodes but rated to much lower voltage. I suspect the change was purely for cost reasons. 1N4148 would have been cheaper at the time.

I prefer to use the 1N4004 / 1N4007 diodes because their leads are thicker and handle playfield vibration better. Plus coils use them too so the one diode type covers both circuits.

You're fine to use any of these diodes mentioned on your switches so if you want to keep all diodes on your Flash Gordon the same, go with the 1N4148.

thanks for the education Safe to assume that the 1N4148 "speed" has no issue with needing to read a quick switch hit of a tilt bob and that "speed" is for much faster Computing situations?

Yep, you got it
1N4148 has a faster recovery time so can support higher speed circuits.