one possibility of the Men who Stare at Goats Mechanic,
is the notion of
1. active concentration DURING staring (build up can be interrupted)
2. a time unit curve:
curve 1. initiative points lost:
bonuses: low
cons: you could get interrupted by someone noticing you staring if they act before your lowered initiative number is reached. Your staring begins at the higher initiative, and your Glaring/Staring has an ever increasingly obvious "notice" bonus to perception or insight checks for SENTIENT creatures.
Animals on the other hand, trigger their fight/flight instincts - some freeze in place, being watched, others realize they are being watched and flee, and more aggressive types begin barking/attacking. Pack animals might howl for backup, or be frightened and flee if the Aura of the Psychic is way stronger than the animals..
Curve 2. Rounds lost:
bonuses: medium
cons: entire rounds are lost. If you are trying to do something, you have to maintain the equivalence of eye contact and uninterrupted concentration. You can possibly move, taking a move action at walking speed, or levitate etc. at similar "slow" speeds, but you can't do stuff like attack or sprint, you are easily flanked, and while you can theoretically walk slowly to hide behind a bush, you must maintain a visual/Sensory path to your target. So you could hide behind rose bushes, or on the other side of a fish tank, but you couldn't hide behind a brick wall. 3/4 cover would be the best you could hope for. Full cover would negate your stare.
Curve 3. Minutes lost:
bonuses: medium
cons: same as rounds
Curve 4. Hours lost:
bonuses: High
Cons: same as minutes, plus a level of exhaustion
Proposed map of scaled curve:
1+2+3+4... because this adds up to +10
thus +4 "somethings" takes -10 initiative.
the next scale is 1 round, 3 rounds, 6 rounds, 10 rounds (i.e. 1 minute)
Bonus/Time: requires concentration, 3/4 or less cover, can only move after effect.
+1, -1 initiative
+2, -3 initiative
+3, -6 initiative
+4, -10 initiative or whole round
+5, 1 round, concentration, 3/4 or less cover, can only move slow, limited actions
+6, 3 rounds
+7, 6 rounds
+8, 10 rounds or 1 minute
+9, 2-9 minutes or similar transition unit; concentration, 3/4 or less cover, + possible level of exhaustion
+10, 10 minutes
+11, 30 minutes
+12, 60 minutes
+13, hours?, +1-2 levels of exhaustion.
What the numbers mean?
Depends on the edition. The above material is crudely setup for 5e. It's saying something +1-12, so perhaps on a skill total equivalent of power?
Example: some large dragon gods have a Passive Perception of 36, so +12 on that sort of scale would require 24 points from someplace else, such as level, attribute bonuses, etc. Some classes in that system have a "double proficiency bonus" so you might see something like 1d20 + 5-10 from stat +6-12 from double proficiency bonus = 12-32.
Put another way, spending an hour straight staring at something for an effect is a +12 bonus. Naturally, if the target moves out of the way, this hour was wasted.
As cumulative bonus Psychic Strength Points:
The scale could be slightly more precise and have even bigger scaling points. Initiative with various bonuses can hit around 26-30, thus going past 10 is possible, especially when you instead of skill equivalent (like a stealth check of 19) you are talking about point costs to active a power, or measure its overall power total. Spell points for higher level spells in Spells & Magic for example, charged 60 points for a Wish, but only 4 points for a Magic Missile. That was a curve from 4-60, with fireball and cone of cold being around 15-20 points.
So the next number after -10 is -15, then -21, then -28. Whatever your initiative is, that would determine your maximum round 1 bonus points (good incentive to take initiative feats).
5 points: -15
6 points: -21
7 points: -28
I don't think there's a point in going to 8 points/-36 initiative, as the stats and dice don't support it, but it's there for reference. When your initiative total drops to 0 or less, your Stare Bumps into "full round/next round".
After that, you might go:
8 points: round 3
9 points: round 6
10 pts: round 10/1st minute
then you have /3/6/10/15/21/28/36/45/55 minutes +9 more, for a total of 19,
and your first hour block is 20 points.
then you have 3/6/10/15 hours, and since people sleep about every 16 hours, we are done, with 24 maximum points,
and 5-7 points maximum within a single initiative set.
There's no particular reason to stick to triangle numbers. We could use anything. Odd numbers, square numbers, 3/5/8/13 numbers, etc. Triangle numbers are just easy to remember and used in 3.5e