you haven't mentioned where the pink tube is coming from, but I'm going to assume it is popping out of the cloaca rather than a nostril or eye socket 
If the tube is pink and has no frilly bits on the end, it is probably one of two hemiclitori. I'd assume your blackthroat is fairly large to have 3" hemiclitori.
If your blackthroat is small or medium in size, you may be looking at one of two hemipenes, in which case 'she' is a 'he'. Immature hemipenes can be pink, rather than purple-ish or blue-ish and if not everted completely may appear as just a tube. Even an adult may partially evert their hemipenes, in which case they'd appear as a simple tube.
Hemipenes are the male's penises and hemiclitori are the female equivalent. They usually rest 'outside in', in the base of the monitor's tail and 'evert'(pop inside out) through the cloaca. Think of the finger of a rubber glove, inside out until someone blows into the glove and it fills out.
People usually see their monitors' hemipenes or hemiclitori when the animals defecate.