On the rear peepsight, (I have one on my takedown) the flat knurled blade at the top may be pulled up to adjust for range.
Apologies if you guys knew this, just saying for those who don’t know.
The bolt does indeed slide over, pushing the peepsight down, then allowing it to spring back into position as it’s being cycled, even when the range blade is pulled up for use.

My M1903 takedown is away at the gunsmith for a while being rebarrelled .. a new Krieger going on and retaining the chambering at 6.5x54 MSch, so kept as a M1903 but with renewed accuracy lasting well beyond my lifetime.

However, Sad to say, the trigger on mine is not sharp and smooth. It’s terrible!
I’m hoping the gunsmith can do something to improve it.
But the bolt action and magazine are truly slick. Smoooooth as silk.

I just bought a very cheap M1903 MSch stutzen. It’s had a nasty scope sidemount fitted to it, with a section of stock cut away to allow the mount to fit. The mount is removed, leaving four horrible tapped holes in the side of the action, and the stock fairly neatly repaired, but visibly so.
I’ll progressively try to improve its appearance, .. But, it’s a shooter! So, I’ll have fun with it.
Cheers.