The Red-Gloved Man with Tommy Muldoon is an incredible pairing. Basically if you can forsee any circumstance where Tommy takes 4 health and/or horror damage in a single go, then the red gloved man will be recycled and shuffled back into Tommy's deck before the Forced event triggers, but will have allowed Tommy to have a whole go of either not getting distracted by enemies; or taking damage and horror to reload Becky. also importantly, given you are using him for a single super-go, you aren't at all worried about the impact of Rookie Mistake), because if you play it well, it will all be sorted before you draw any cards in the upkeep phase.
Examples below are just from Night of the Zealot enemies, so there are a couple of spoilers if you read the text here and haven't yet played Night of the zealot scenario 1 - the gathering. (and if you haven't done that, why are you reading about 5xp cards anyway? ;-)
1) Tommy just has a single simple enemy but has things to do; not many resources; or has Becky deployed but on zero ammo. (say you are facing a Swarm of Rats or if you are lucky one that does 1 damage and 1 horror, such as Ghoul Minion).
If Tommy needs to progress the scenario quickly and get ammo back on Becky: Play The Red-Gloved Man to enable Tommy to just investigate three times (at skill level 6) or move through a few locations. He takes a total of 3 attacks of opportunity and another attack during the enemy phase, so the The Red-Gloved Man is defeated and shuffled back into Tommy's deck; (to quickly fight another day) and Tommy gets either 4 or 8 resources / ammo as well as a good chance of getting three clues or moving or otherwise maintaining tempo.
e.g. 2) Tommy has Becky in his hand, but not in his actual hands yet. He's got a lot of resources. He's surrounded by three enemies (Swarm of Rats; Ghoul Priest; Ghoul Minion, which would be doing him 4 damage and 3 horror every turn. )
Action 0(fast) Play The Red-Gloved Man, give the base 6 stat boost to Evade and to Fight;
Action 1 Fight (with fists, helped by Red) the Swarm of Rats (total strength 6 against difficulty 1). hopefully kill it
Action 2 Play Becky (which attack of opportunity from the two ghouls puts 3 damage and horror to Red)
Action 3 Evade the ghoul priest (skill 6 against difficulty 4)
Enemy phase sees the Ghoul Minion attacking Red, defeating him, and shuffling him back into your deck. you then get 8 resources back, some of which you are likely to want to put on Becky, to help the next round's combat against the ghouls.
Next round, instead of facing three enemies with no weapons and no chance, you now have Becky with anything up to 10 ammo on, just ready to start unloading merry hell on Ghoul Minion and Ghoul Priest.
If you are really lucky, you'll have a seeker with No Stone Unturned at your location to get The Red-Gloved Man straight back into your hand before your next turn!!
Much more simple but similar to example 2: you have a single big enemy (one that does at least 2 damage and/or horror) again from the Gathering example, lets just go with Ghoul Priest and don't yet have Becky out!
Action 0 fast: play Red
Action 1 Play Becky. (Red takes 2 damage and 2 horror)
Action 2 Fight Ghoul Priest using Becky (1 ammo now left). strength 8 vs 4.
Action 3 Fight Ghoul Priest using Becky (all ammo used up). Strength 8 vs 4.
Enemy phase defeats The Red-Gloved Man, putting 8 ammo back onto becky.
For round 2, you have masses of ammo on becky, you have 0 damage against you, and you are ready to fight three times against Ghoul Priest before you even begin to worry about taking attacks. In both turns you have a pretty good chance of dealing 10 damage to the ghoul priest in 2 goes, without worrying about receiving any damage.
Basically The Red-Gloved Man gives you something that all good higher level cards give: Tempo. But with Tommy Muldoon you get the Triple-whammy of Tempo, recursion and resources/ammo.