Nice problem!
There are a number of ways of achieving this. It depends a bit on what kind of line or drawing you need. If you are after a straight line, then it may be worth it while to insert a color bord in the track underneath your clip. Then change the color bord into a line, you can get to (almost) any thinness and size, and position and rotate the line anywhere on the screen.
Another method would be to draw the line precisely as you describe. And save that line (give it a name etc.)
Put the line in the track underneath the clip and then position the “cursor” to a point where the line has been completed after drawing.
Then select the clip above and set the opacity to 0% by dragging the opacity line down. What is left (in the preview screen) is the complete line. Take a snapshot on that position. (The alternative is to put the snapshot on a place where there is no clip and take a snapshot of that....)
Delete the drawing from the track and replace it with the snapshot, which can be given the required start- and end point and length.
Then open de PIP designer and set a chroma key for the (black) background and close the designer. Because the snapshot shows the result of the drawing not the drawing itself, you end up with a line that can appear and disappear at will.
I am sure that there are other ways of getting what you want, without the help of external drawing software. The methods above did not take much time to execute.
Have fun!