The 617.95 FSM tells a different story. Normally, only one failed glow plug will trigger the fault indication. In extreme cases, two failed plugs may be required. For sure, failure of the #1 glow plug should trigger the fault indication under any circumstance.

Glow Plug Relay /Timer
 

I've timed them several times and every one was 30 seconds of current to the glow plugs, the indicator lamp goes out sooner .

There's an adjusting screw with 10MM ATF jamb nut on it, I've never touched that .

I've had a few of these relays fail, because they're over $100 I bought used ones and so far so good, twenty years and counting .

Can a faulty relay cause this issue as well?

G.P. Relay
 

I don't know ~ I've had one glow plug fail and cause the lamp to blink, another time the light didn't come on at all for one glow plug gone open circuit .

This presumes parallel glow plugs ~ the series ones you loose one plug it's the same as all = open circuit .