I think those repro's are copies of a "sniper safety" - allows scope to sit much lower than regular m98 safety. The one that I have was a simple "drop in" replacement for an original m98 safety into the military shroud. Not at all "handy" to use - I can not operate one without using my thumb and finger to grasp it, so pretty much have to let go with shooting hand to grab it and turn it, in order to fire.
I have installed two of the horizontal swinging lever three position safeties - one was a "Dakota" and one was a "Gentry" - they work just like those on a Model 70 Winchester - requires careful marking, grinding a U-shaped notch into the bolt body, work very well when cocking piece, sear and that safety all fitted correctly together. Not really "drop in". They replace the military shroud completely.
You mentioned that you installed the Timney and it is "stuck in the down position" - you might realize that a mauser 98 safety can only be engaged when the rifle is cocked? The down position on a Timney safety is the "fire" position, and is supposed to allow the cocking piece to travel forward. If it is cocked and still "stuck down", not certain at all how you re-installed the firing pin and cocking piece, after installing the safety? A gunsmith who is familiar with the mauser system should have no problem fitting a Timney safety into your rifle. If someone, or years of wear, has ground or altered the sear or its engagement surface on the cocking piece, then it is possible a small bevel may be required on the leading edge of the cocking piece shoulder, where the safety's bevel will cam. Big letters on the Timney instructions - DO NOT GRIND SAFETY.