K1000 service manual is here:
http://www.pentax-manuals.com/markroberts/k1000_man.pdf
[EDIT: seems to be an "unofficial" service manual, it has a nice didactic character]
I suppose that there is a problem with the speed resistor. If I get it right, when you select a shutter speed a resistor of a certain value is in the circuit and when you change the speed a resistor of a different value is inserted in the circuit. There is also a variable resistor for the aperture value and there must be, presumably, another variable resistor for the film speed (or probably there is a trick that uses the same resistor for film speed and shutter speed, if they are coaxial). The resistors make the needle move up and down in the screen. The exposure is "correct" when the needle is horizontal, at the center of its possible run.
The case may be that the resistors for 1/500 and 1/1000 have a problem (broken or bad contact). A repairer should check the resistors of those two speeds.
The competing Minolta SrT-100x has a light-meter needle which moved along the entire span (high or low depending on how much light there was) and an
ago pedinatore (tailing needle?) which is connected to aperture, shutter and film speed. Exposure is correct when the two needles are at the same point (which can be high, low, middle). The Minolta scheme is mechanically more complex and electrically less complex. Presumably the SrT solution is more prone to problems in case of shock but less prone to problems of oxidation etc.
The service manual might help in opening the camera and cleaning electrical contacts inside, maybe. A repairer is always a better solution, a good overall cleaning, lubrication and adjustment. Let's keep repairers in business!