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but like how close is close enough for alignment for an exposure to not trial at equatorial region by so much and with a 10" F10 instrument for anything over 3 minutes (roughly). Does anyone know? Thank you
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Very roughly, if the polar axis is offset 1 degree in azimuth and you start tracking with a star on the celestial equator and on the meridian, six hours later it will have trailed 1 degree in dec and obviously a little in RA. So it will trail approximately 1 arc sec per minute per degree offset. It is more complicated than this especially when the offset has altitude and azimuth components but it sounds like this is the sort of rough number you are looking for.
The plate scale of your scope is ~ 12 micron / arc sec so over 3 mins it will trail 36 microns. That's eight pixels of trail for a 4.5 micron/pixel camera.
At that scale an autoguider is pretty well essential.
Joe