You know, I'm still pissed they canceled Megaman Legends 3. I was looking forward to that... Granted in my present state I probably wouldn't have gotten to play it anyways but... it's the point of the matter.
Anyways, not here to talk about vidya gaymes... that just sounded like a good stupid title to go with the rest of them.
Now, I'm making an big EverymanHYBRID reference with this one, but "Sigma" is essentially a form of... Radiation? That was first detected in a sliver of black "material" found by Dr. Corenthal and delivered to a specialist in... ahh... elemental... stuff. Wow, I forget small details really fast. Point of the matter... the material is believed to be some "part" of the Construct which was left behind during one of his visits. This wouldn't be the first instance of the Construct leaving behind one form of ectoplasm or another, so sounds plausible enough. Anyways, having detected and identified this new form of radiation, dubbed "Sigma," they were able to build a device which could detect the radiation. The EMH boys found this device and inevitably discovered how it worked through... ahh... "unconventional methods of testing." After which they confirmed that each of them had Sigma Radiation in their blood.
So... what is the point I'm getting to with this? Well, whether you believe specifically in the existence of "Sigma" or not, it is still a very viable answer to the question of how the Construct tracks his victims. Previously, I've referred to the concept of the Construct "marking" his victims. I couldn't say how he does it, but the point of the matter is that once marked, it's like you've got an active homing beacon on you. It doesn't matter how far you travel or where you hide, the Construct will find you. Sigma Radiation is simply one means of explaining this. (It's also probably a good explanation for why people in contact with the Construct have a tendency to get sick... You know? Radiation poisoning or something? Meh, topic for another time.)
Also, with this explanation, comes the possibility of a means of evading the Construct. By dampening or outright removing the radiation, the tracking beacon, you could potentially "lose" the Construct and render him unable to track you. However, this assumes that the beacon is something as simple as "radiation" or "pheromones" or some other naturally occurring "thing" which could be used as the beacon. It would require experimentation that I have no means of conducting however... BUT there have been cases of "cures" in the past, so something of this nature does seem possible.
Basically, just so long as the beacon isn't a literal "psychic" mark, then presumably it could be eliminated via some natural means. Your body might even be capable of removing the toxin on it's own over time, provided you were able to evade the Construct for long enough. (Perhaps why/how many young children who were exposed to the Construct were able to escape from him. The infection was not yet strong enough to track before they were moved to a new location outside the Construct's grasp?)
It is still possible however that the beacon is more supernaturally based. I'm leaning towards some form of psychic link, especially given the occasionally touted "hivemind" between Contruct and Proxy theory. Something like that would be a lot harder to remove. Short of being someone really well experienced and learned in that kind of... Activity. And even then it's questionable if such a thing could be removed.
However it works, I do believe that the concept of being "marked" is a sound one. And that once marked you're pretty much screwed. Especially given that prolonged exposure to the Construct likely strengthens the beacon over time. But there is evidence that the mark can be removed. It's just not very easy...
Perspective is Key.