TLTeo

Alright I did some more testing:
1) I re-opened the track I attached, in which I swear to god the ILS needles didn't show up while I was playing. This time they did, in agreement with Kotiuka's post. Yay for me not going insane.
2) I then re-launched the same mission, ILS needles showed up again.
3) I tried the landing mission in Syria instead (at Ramat David), ILS needles didn't show up.
4) I re-started DCS and tried the Syria mission again (without loading the Nevada one first), the ILS needles now did show up. So at this point, either loading a new map or tuning into a new station causes the ILS needles to not show up.
5) I then re-started DCS once again and tried a quick mission where I spawned at Akrotiri near final, turned on active pause, tuned into the ILS, then flew over to Paphos and tried the same. The ILS needles showed up both times.
So it looks as if the ILS beacons are not being recognized if you fly on multiple maps, only the ones in the first map you load are "found". This is also consistent with why I made this post in the first place - I completely botched an ILS approach on one of my own missions in Syria, and decided to practice in the Nevada landing missions.

My crappy order of magnitude estimate was here:
 
for reference, the ~2 degree error I worked out would produce an uncertainty of ~1 nm on the location of the SAM, if looking at it from 25nm away (taking just delta_L = D*sin(theta), where theta is the PSF of our detector, D the distance of the emitter, and delta_L the uncertainty on its position). So basically in the Hornet in TOO, you would get your target box in the HUD, point your TGP at it, and have the same could be anywhere 1nm to the left or right of where you have pointed the FLIR. And that obviously neglects the fact you can't estimate distance either, so you would have an even bigger area to search.
Instead in DCS, we can point the TGP at the box in the HUD and always instantly spot the SAM site.
 
edit: to avoid derailing the thread and asnwer the OP, at what time of the day were you flying? I noticed the lock range of the Walleye is a strong function of time of day rather than light conditions, even though the scenario may look the same between, say, 7 and 8 am. The -H also has a TV sensor, so maybe that's what's going on.