Thanks shutterfinger but are you saying that I should cover the eyepiece from before the shutter is tripped, keep it covered for the entire duration of the self-timer (about 10 seconds regardless of shutter speed) and then keep it covered for the additional time that the shutter is up during the actual exposure?
Thanks Chan Tran okay I had not even thought of this aspect! So it's not a concern about light coming through the viewfinder and hitting the exposed film, but about light coming through the viewfinder and hitting the cameras metering system causing a change in the suggested shutter speed or actual shutter speed if using auto mode.
Thanks fish of the day

I believe with the Nikon Fe the exposure is locked when you use the self timer, and also you can lock exposure when not using the self timer using the same button.
Really I'm trying to avoid the awkward maneuver of keeping the viewfinder completely free of penetrating light for the complete duration. It's a bit of an awkward thing and the better I am at blocking light, that is the closer I am to the viewfinder with my finger or hand or whatever, the more likely it is that I will touch the camera which obviously I want to avoid. We are talking about something more than 10 seconds for the duration of the self-timer regardless of shutter speed.
So if it is truly only a question of the light coming through the viewfinder and affecting the meter, that's great and I can deal with that and that means only protecting the viewfinder from light during the setting of the exposure. Usually my face will be crammed up against there at that point anyway. Then I can trip the shutter and safely move away from the camera and wait for the 10 seconds of the self-timer and then the exposure and be done. On the other hand if it is a question of light coming through the viewfinder and reaching the film then I want to know if that is just when the shutter is tripped at the end of the self timer or during the entire 10 seconds of the self-timer when the mirror is raised. It looks like we have two votes for the former possibility.