At its heart, the GUMSHOE system boils down to the following:
Gathering clues is simple. All you have to do is: 1) get yourself into a scene where relevant information can be gathered and 2) have the right ability to discover the clue and 3) tell the GM that you’re using it. As long as you do these three things, you will never fail to gain a piece of necessary information. It is never dependent on a die roll. If you ask for it, you will get it.
This ethos can be applied to other game systems pretty easily, without bringing in the supporting structure of ability pools that traditional GUMSHOE uses. Many other systems have traits that are useful for gathering information. If a player finds themselves in a scene and describes how their character uses one of these traits in pursuit of information, the GM can just give their character the appropriate clue if one is there to be found. Don't rely on a roll that could fail and leave the characters without necessary information.
And it's true — you may already do this in your system of choice!
One element of GUMSHOE that might require some adaptation into your favorite game is the ability to spend points from an investigative ability to gain some benefit. If you want to include this feature in your game, you can just assign a certain number of uses per scenario based on how highly rated the character is in a particular information-gathering trait. Each use should give a bonus to a more active trait or provide a narrative benefit like gaining a temporary ally or declaring facts about the scene.