PULSE WAVE Give this character a ranged combat action; it can use
<new ignoring terrain symbols are shown here> and halves its range value until the action has been resolved. Draw lines of fire to all characters within range in every direction, including at least one opposing character. All game effects possessed or used by other characters with a line of fire drawn to them are ignored until the action has been resolved. If ignoring a game effect would cause a character with a line of fire drawn to it to no longer have a line of fire drawn to it, then it is not ignored. If lines of fire can be drawn to two or more other characters, this character’s damage value becomes 1 and is locked. Make a single ranged combat attack and compare the attack total to the defense value of all other characters with a line of fire drawn to it; each character hit is dealt damage.

Emphasis mine. I put it off to the last minute, but hopefully I can get this answered overnight:

If someone is outside the Pulse Wave'ing character's range, are their game effects ignored as long as the Pulse Wave'ing character can draw line of sight to them? So, for example, no Probability Control even if the PC'er is within range of PC but outside the Pulse Wave?

It looks like modifiers are not ignored, so if someone Perplex'ing a defender's defense is hiding behind a wall, the defender still gets the modifier to his/her defense, correct?

Any help you can provide would be appreciated. Thank you for your time with this and have a great evening!

If the character is not within half your character's range value, then it does not have LOF drawn to it. No LOF drawn to it = nothing is ignored. Using your example, the PC would be fine to use as it is coming from outside the PW range.

Modifiers are ignored if the effect that caused the modifier is within the PW range and has LOF drawn to it. In your example, the wall would block LOF, so Perplex is not ignored and the modifier stays put.

Thanks for the response!