This code:

# Flash that LED
gpio.output(led, gpio.HIGH)
time.sleep(0.2)
gpio.output(led, gpio.LOW)

is the bit that turns the LED on for 0.2 seconds, then off. You can make it stay on by increasing the number from 0.2 to 2 (for 2 seconds) or whatever suits you.

Be aware that while this bit of the program is running, it won’t be actively looking for more matching tweets, so may miss some. The longer it waits, the more likely it is to miss them – this may or may not be an issue to you!