Well I don't know if this will truly help, but Big Book of Amiga Hardware had this to say about the 1950.
"Common Problems
A sync problem may be caused by the monitor detecting sync on the Green input and then disabling the horizontal and vertical sync inputs. Removing the 10K R854 resistor or the 10uf C812 capacitor on the small vertical board may fix this. It may also cause problems of its own, so be warned. The analog/TTL switch appears to be prone to failure. However, if switching the switch brings back the picture, it may actually be that the 74LS123 (IC805) on the same board is failing. The suggested course of action is to replace (or at least resolder) this chip first, since it's a commonly available part. A defect in the way the 74LS123 is mounted may be present; there should be +5V on pin 3, but the way the chip is mounted or the board is manufactured, it may be intermittent. There should be a PCB trace between pin 3 and pin 16, however, pin 3 is not soldered to this trace, but only friction-fit (non-plated-through holes?). When the analog switch is moved, it causes intermittent contact between pin 3 and the trace. A soldered jumper to pin 16 is an easy way to fix this, or you may be able to solder to the trace already present. Another common problem is the failure of a multifunction sync chip. Replacements should be available from Sony. The high-voltage boards may crack; this can be one cause of the monitor that starts working when you hit it. A 1 megohm resistor in the second power supply's startup circuit goes bad, causing the monitor to remain dark. Replacing the resistor with a higher wattage one may help prevent the problem in the future."
If I understand what they are saying, it appears that a syncing problem is a common issue with the 1950 monitors. Do you have any 1084's or other commodore monitors you can check to make certain that there isn't something wrong with the video output? Also you might want to check and see what monitor you are using in the prefs screenmode section. Might be set from something that won't display on that monitor.
