It's an old idea: Pioneer and later spacecraft have a plaque showing our location relative to distances to pulsars we can see from Earth.
https://en.wikipedia.org/wiki/Pulsar
https://en.wikipedia.org/wiki/Pulsar#/media/File:Pioneer_pla...
edit: I guess if you're a Type 3 civilization with nothing better to do, you wouldn't have to set up lighthouses but you could better direct your attention to moving galaxies around or whatever.
There's work towards this, from the X-ray emission of pulsars[0]. I don't think you'd need a precise distance to the pulsars to measure your own position, as long as you're measuring your own position relative to some other object (e.g., Solar System barycenter). If it's a relative measurement then you should be able to determine that by comparing the time-of-arrival (TOA) of the pulsed emission from multiple pulsars with the TOAs at Earth.
[0] https://en.wikipedia.org/wiki/X-ray_pulsar-based_navigation
I'd worry about pulse identification over any significant period of time.
But I don't think these things would cripple a pulsar-based navigation system. Presumably any network of pulsars used for this purpose would be regularly monitored and timing solutions would be updated regularly. The updated timing solutions could be transmitted as-needed.
At any rate, a robust navigation network of pulsars would need a sufficient number of sources to guard against glitches breaking the navigation system.