As GW says, you'll need a 2:1 shifter.

SRAM shifters with names (Attack, Rocket etc.) are shimano compatible.
SRAM shifters with numbers (x9, x7 etc) are not shimano compatible.

As above, but have done it on a DH bike. IIRC I have a rocket shifter.
Ran a Grip shit and Dura Ace rear 😯
Now same grip shift and rapid rise LX shifter, I use ODI lock-ons as they have a short version for the shifter side.

For downhill it's ace, I can keep a death grip on the bars, and with the rapid rise as I stand up (and rotate wrist forwards) I can slide into a lower gear, as I launch or get off the back going into a faster section I can pull into a higher gear.

But, elegant it is not, the grip is grubby and the little indicator window doobry doesn't work any more (bike is ancient mind).

Can sort of see it here:

andyfowler, if you click on the linky in my previous post, it will take you to the SRAM webpage listing their 2:1 shifters. There's three 2:1 shifter types: Attack, Centera and MRX (there used to be a Rocket shifter as TheChunk has already mentioned).

All these have gripshift options but I'm not sure if they're all suitable for MTBs or for town bikes etc. I'll leave it to you to go through their product manuals given on the webpage.