I'll take a bet with you - your truck is a grey market import - right or wrong?
The onus is on you, before buying a vehicle to ensure that after purchase support will be available, which is something you didn't do before purchase, and the reason I know this is because you're complaining about it after the purchase.
If you had checked - this is what you would have found out - service documentation for used JDM vehicles is almost impossible to locate, and when available it is in Japanese. By service documentation I mean service manuals which document the procedures and specifications, and also part catalogs - even the dealer diagnostic tools, don't work on the JDM cars.
Suzuki just does not make this information available outside of Japan.
Put your self in the dealer's shoes - and let's give them the benefit of the doubt, they would like to help you, but you're bringing in a vehicle for service, which outwardly resembles the ones they are selling, but when they open the hood, it's different.
Do they have the oil filters in stock - maybe/maybe not - and oil filters are a part that should not be fitted based on appearance, just like the car, the outside looks the same, but the inside may be different. Do they have the air filters in stock - maybe/maybe not - I've seen air filters that look alike (even bought them) only to find they're an eighth of an inch too thin and don't seal, do they have spark plugs in stock - what plug does your engine take again?
Don't blame the dealer - you didn't buy the car from them - why aren't you taking the car back to the person you bought it from?
Like you, I own a used JDM car, not a Suzuki in this case, but the story is the same regardless of manufacturer - if you weren't aware of it before, you are now - buying used JDM is cheaper, but has it's problems, and even if the dealer wants to help you, he may be unable to, because of a lack of necessary resources & information.
And no, I don't know where you can source the parts from or even what part numbers you need, but if your vehicle was not JDM, I'd be able to look it up, just like your dealer would.