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It sounds to me like you have drawn a path on a solid, applied the stroke effect, then animated the stroke. You've also copied the path drawn on this solid and pasted the info to the position property of your brush layer. If that's the case here's a few things to think about.
First, when you copy a mask path and paste it to any position property you end up with a start and end keyframe with a bunch of roving keyframes between them. Roving keyframes are indicated in the time line by little dots. You change the timing of this position animation by selecting the ending keyframe and dragging it around the time line. When you do this all of the roving keyframes automatically adjust to maintain a uniform speed.
Second, when you select all of these keyframes and apply Easy Ease the roving keyframes change to bezier keyframes and are locked to time. This means that the time between each keyframe has an ease curve applied.
Third, if you apply easy ease to the stroke end (or start) position you have only 2 keyframes. The temporal curve (see the graph editor) between these two keyframes cannot match the temporal curve of the Brush Graphic position unless there are only 2 keyframes that property.
Fourth, you have to decide whether you'd rather have easing between the each of the Brush Graphic position keyframes or easing just between the starting and ending of the Stroke effect you're using to reveal the image. If you want easing between each of the Brush Graphic position keyframes then you have to add a keyframe to Stroke End at exactly the same position of each Brush Graphic keyframe and apply easing to all of them. If you only want easing between the stroke start and end keyframes then you have to change all of the keyframes between the start and end keyframes back to roving keyframes.
You can use the keyframe interpretation tools to convert all keyframes in the Brush Graphic comp to Roving keyframes by selecting position, then Keyframe Interpolation, then Rove Across Time. This should make the graphic line up nearly perfectly with the stroke effect. It won't be perfect because there may be some imperfections in the bezier curves of your mask path that cause calculation errors when the curves are converted to position. In most cases the animation will be close enough to hide the errors.
If you decide to try and match the easing between each Brush Graphic position keyframe you will have to insert a new keyframe in your Stroke End property for each keyframe in the Brush Graphic. This also will not be completely accurate because when the roving keyframes are converted they are placed at an exact moment in time instead of an exact frame. The process is also tedious if your path is complex.
The only way to perfectly match the position with easing would be to pre-compose both layers before any ease is applied, then time remap the pre-comp and apply keyframes and easing to the time remapping.
You can also simplify your project by applying the mask path directly to the image you want to reveal and selecting Reveal Original in the Stroke properties. This would eliminate the track matte and make manipulating the keyframes for Stroke and the Brush Graphic much easier.
I hope this makes sense to you.