You know what? Let's get abstract!
It all depends on the nature of signal detection and signal propagation.
You know what you said about triangulation? That's required if your detection method returns a direction but not a distance. For instance, when a submarine detects a sound from "heading 281", they don't necessarily know how far away that noise is. So they run a bit in a perpendicular direction, then stop - and use the difference in headings to roughly triangulate where the sound came from.
But if a submarine 'pings' its target, it not only gets the bearing, but the distance as well - based on the time it takes the sound to echo off the target and return back to the originating pinger. Triangulation is not required there, because the information being returned includes both angle and distance.
So, let's start taking a look at options.
Signals have a direction but no distance. For instance, someone emits an electromagnetic signal and someone else detects it. Or they emit a FTL version of that signal. The receiver is getting an angle to which the signal corresponds. So how does one indicate their position? Easy: just include within the information on the distances to two nearby celestial objects. After all, the receiver could trace back where the signal came from, and there'd only be two possible points on that line with a distance X from object Y. If they give two such distances, that narrows it down to one specific point. Aka, a distress call would be, "I'm 1.98 floobars away from Omicron Alpha 7, and 1.99 floobars away from Omicron Alpha 8."
Signals have a direction and a distance. For instance, someone emits a signal that has a half-life depending on distance. The receiver gets both an angle and a direction - basically, the same information as a submarine ping. In that case, there's no need to transmit location information at all. (Just like a submarine doesn't need anything more than a simple 'ping' sound to get what it needs: the signal itself is good enough.)
Signals have a distance but no direction. Aka, an ansiable network that has a half-life depending on how far away the signal came from - but there's no telling which direction the signal came from. This is when triangulation comes into play. In that case, the best solution is to have three detectors working in concert, using the distances of each to plot a point in 3D space where the signal came from. In that case, there's no need to transmit location information at all - you'd be relying on the detector to do the legwork of triangulating your position.
Signals have neither a direction nor a distance. Aka, an ansiable network which just 'is' - it's like a bulletin board where posted messages just appear and you have no clue where they came from or how far away the poster was. This is when things get tricky. In that case, you have to perform the triangulation yourself. If you list your current distance away from 3 known stellar objects, that will be enough to triangulate yourself to anyone knowing the position of those objects. In which case, a distress signal is you listing your position in regards to three stars/etc.