There's 'turner's tape', a seriously sticky double-faced tape available at woodworker's stores, such as Klingspor. 1" w. typically, grey, leaves no residue, typically used to stick wood to lathe plates (albeit generously in that application). If I want something to 'sit and stay' until I say 'move', that's my goto.
If you desire something more aggressive, there's 3M's VHB tapes available from Uline. You can pick widths and degrees of 'sticky', foam or film. BUT...VHB's can Really Be Strong, to the point of permanence. If you opt for a foam carrier, you can slice it apart with a razor blade and rub it off the surface with your fingers (it's a rubber based adhesive that'll 'roll up' like rubber contact cement...but won't be quite as quick to do so...your finger tips will complain about it....)
And there's always a dab of clear silicone adhesive. Acts like the VHB, but can act like a rubber 'foot' if you let it set up awhile first...