I'm going to assume an XBox console and the remastered version and using the Default Configuration config file. There are several different versions and supported platforms for that game and they are all different in their controls.
There is no function that would pulse an output twice after a delay. The delay will need to be done manually with a second input.
I think you could use a mode sheet set up like this:
X, delay_off 500, mp_center_sip
right_joy_up, pulse 100 2, mp_center_puff
Start with the sip, then switch to the puff at the right moment. The X button will be held on during the puff and two pulses flipping the joystick up.