Did you ground the glow plug that you tested with?
Try cleaning and tightening the connections at the glow plug relay. Could be a bad relay, but try cleaning/tightening first. I have seen threads about people changing out to manual, but generally speaking the relay is pretty reliable. There's a good chance the one you have is original - can't argue with that lifespan.
1998 K2500 Suburban 6.5L TD 3.73 rear, Ron Schoolcraft 18:1, Kennedy ECM & IC, Timing gears, Splayed main caps, 3.5" Kennedy Exhuast/No Cat, K&N Filter, Boost/Tranny Temp/EGT(Pre Turbo), Ceramic-coated Manifolds, 195 Stat's, 265/75's (VSSB Adjusted) 7,000lbs (on a scale) Remote Mount Oil Filter, Remote Oil Pressure Sensor