Questions on Stealth and the Map

I haven't been able to test this fully because I mainly play solo, but due to my experiences I am now under the assumption that crouching and going stealth removes your dot from other players map, even if you walk as long as you don't hold down run or sprint because you will notice if you crouch your own icon on your map changes to a dark grey instead of the usual white. It only seems to turn white when you run while crouched or sprint. I have no way to confirm this aside from the fact that stealthing seems to have made it far easier to catch PVPer's off guard and take them out before they even notice me, but maybe they were just not paying attention to their map.

I would like if anyone can confirm this and/or go into more details, but also I want to know if it works if you have already been in a fight with the person. Since once someone kills you or you kill someone, the red dot becomes a deeper red and it also shows their general direction, does stealthing still remove the dot but just keep the red line on the radar? Any confirmations would be nice, thanks.