His entire focus is on gaining the personal skills to be faster, more cunning, more deadly and more resilient in both melee and campaign warfare. While Kamilata is in managing the defence of the static lyrond (a good ex-jalee role), Tud is out arranging the irregular distributed warfare defences of his lyo's lands (a good ilin role). Despite carrying really quite serious injuries. When other ilin are about he will be training them in the terrain, in ambush points, routes, places to shelter, caches, the vegetation, the landscape, the people, the threats, and so on. If/when he takes them out into the wilds he will drive them hard, and they will come back weeks later hairy, filthy and exhausted.
He's probably (Thranduil included?) the most infamously deadly all-round warrior amongst the characters, especially given he won't run out of power points. And despite a rather unlucky recent injury, which his lyo is oddly letting fester... Given his history - he has after all walked amongst the gods, across worlds, used magic, is well versed in advanced steam technology, had an arm turned into the sword of a god, amongst other things - an eye for shiny things, trophies and a rather cavalier attitude to supernatural 'taints' are not bad going. And all his shiny things go towards developing his ability to be really /really/ ilin; apart from a brief stint in the Iron Kingdoms when the ilin structure collapsed, there's no /personal /power or 'wealth' developed; Kamilata and his established position as regent-in-lyo-absence is much more 'dangerous' if you go that paranoid route. Unlike most ilin Tud appreciates the value of money in order to get things to happen outside the normal illin/empire structures, but it all goes into the job.
Tud's rather single minded focus on his job includes a binding loyalty to his lyio, but bear in mind that he's had other lyio that are 'properly' respected so he can obviously compare her behaviour to theirs. And all the older characters have a long history with her as a relatively junior member of the party, which includes behaviour (eg as undead in the Iron Kingdoms) that would normally be fairly fine grounds for ilin loyal to the empire to not just abandon her but try for a mercy killing.
His current lyio has shown little or no loyalty to the empire, to the ilin codes, no responsibility for the lands she is supposedly responsible for, or indeed her ilin. She has the command, but is yet to earn any /respect/. So Tud's loyalty to Forgeillil is to the letter and based on his strong ilin values. But she has yet to take on the role of lyio as well as the mantle - say, by collaborating on a set of defence strategies and tactics, training a reserve local militia force since most of the effective force is usually absent, or pretty much anything beyond her naked ambition and venality (heh). Otherwise, in the meantime, Tud will continue to exercise his ilin skills to the full and for his lyio with little regard to /who/ holds the position of his lyio; given past experience (!) he expects to die in service to her.
If that service includes tattoos or piercings or anything to improve his performance in the field (say, to increase range, stamina, strength, health, sneakiness) then he'll not only go for it but encourage very strongly the junior ilin to do so as well, and that will hold some weight. Obviously if Forgeillil bans things he will follow her instructions, but (especially) if it's given as some arbitrary imperious edict he will do his best to reduce the effects they have on getting his job done to the best of his ability and those around him. The older characters are used to working that way anyway.
Tattoos, for example, might be 'just not ilin' but it's only the soft, safe, court ilin who can afford to ignore such tools. Though many might not take up strange things for traditional cultural reasons, frontline ilin like Tud have a job to do, and /his/ culture has been broadened a /lot/. Treat it like, perhaps, eating dog in our culture; we might frown on it or even think it horribly disgusting, but anyone as focussed and hairy as Tud who has lived amongst dog eaters is not going to be put off by such nancy provincial attitudes, and he won't have much patience for them either. Anyone who tries a jeer or a spit is likely to get a warning clout through both ears.
Some interesting and valid points. My two immediate observations are that all ilin expect to die in service to their Lyio. And that Tattoos are in this context not 'a tool' but more of an identifying mark of a long standing enemy. I'd love to know what the other PCs think.