There are certainly plenty of photos of ion engines being tested in vacuum chambers, and certainly if you look up into them from some limited range of angles there is relatively bright light from the plasma. So there's going to be a cone of directions behind the thruster where the signal is optimal.
Images also show a more "ghostly" trail of glow from the engine's exhaust extending some distance behind the engine that can be viewed from all directions.
The details of the brightness and the length of this "omnidirectional" tail (except not viewable if the spacecraft is pointed straight at you) depend on several things - the engine power, the gas species (xenon, krypton, argon, iodine1 (solid sources have advantages over heavy pressured bottles) etc.) and the lifetime of the excited state if the ion is leaving the engine excited.
Of course in the near-field plume where the electron and ion densities are still high, there is also light generated during electron-ion recombination.
There will always be a thermal infrared signature
If you have an engine that uses say 1 kilowatt of power, almost all of that goes into waste heat - so there will be a very distinct thermal signature and those thermal IR NEO asteroid-hunting telescopes will be one way to detect them. Ion engines use accelerated electrons (usually) confined in a magnetic field to hit neutral atoms to ionize them. Power is applied (usually) via radiofrequency (MHz to GHz) transmitters that are fairly efficient but much of this plasma heating is transferred to the walls by collisions (ions or energetic electrons - they have to go somewhere) and radiation.
There will be very distinct and non-star-like narrow spectral features
Depending on the type of gas atom and the average energy and number of the electron impacts before the ion gets accelerated and escapes, the ions will enter space in an excited stated. The'll have a transverse sort-of-thermal velocity spread of 100 to 1000 m/s and a fairly narrow backwards velocity spread of 10,000 to 100,000 m/s.
If you are an astronomer and you are using a filter for Xenon wavelengths or wavelengths of another gas being used by the engine, you'll see a dim point of light with a very peculiar temperature (you would interprate it that way) of say 200 to 1000 K, and a Doppler shift of ± 30 to ± 300 ppm that had a very fast proper motion compared to astronomical objects.
The ± comes from the exhaust velocity times cosine theta.
In other words, if you are already looking for a weak source of light at a wavelength corresponding to the ions present in the thruster's plasma and exhaust, you'll see a fairly narrow spectral peak, strangely shifted in wavelength and moving pretty fast across the celestial sphere relative to the stars.
Actually "seeing the light" depends on distance and telescope-pointing
A 1 kW engine might make as much as 1 watt of isotropic narrow-band light at most, though "you mileage may vary" substantially. That's 2E+18 photons/sec. If you have a 3 meter telescope and can find and track objects in low Earth orbit at say 500 km, (a tall order) you can pick up a million photons per second. That's a lot of light for an astronomer! So if you already know what to look for and roughly where to look, it's certainly possible. And the details of the spectral peak and how it shifts in wavelength and brightness as you view it from different angles as it passes overhead may give you some engine technology identification information. Maybe you can even get some kind of satellite fingerprint if you're clever.
Of course if the satellite is in daylight rather than Earth's shadow, it will reflect a ton more light than that. So if you want/need to see the engine light, you have to look when the spacecraft is in Earth's shadow.
If your spacecraft is out at GEO that drops to about 1000 photons per second, and near the Moon it's down to about 1 per second.
Since the spectrum is very narrow and the Doppler shift is predictable, that would be technologically doable but really hard and expensive.
1https://space.stackexchange.com/search?q=iodine
