Extremely context dependent. How much card draw do you have, how many Preordains, he many tutors and what kind, do you even have a use for off-color Moxen or grindy utility trinkets...
Excellent point. I suppose I've been thinking from the mind set of Force of Will, for which I've seen a lot people claim there's definitely an absolute minimum of blue cards to run.
I've never run Tinker in a deck with less than 8 (moxes, lotus, crypt, sol ring). That's probably less a factor of how many artifacts you need, than the fact that mana artifacts are typically good with the kinds of strategies Tinker is good with. You could probably get away with a few less.
I know it's fashionable right now to run fewer Moxes, but I would consider running more just the two on-colored ones. I don't know what your deck looks like, but it's hard for me to imagine a successful control deck with a curve low enough to not want any off-color Moxes. Without cards that cost 3+, a bunch of removal and counters won't get you anywhere against the popular decks right now, which have a lot of card-advantage baked in. This may not apply if "a lot of control elements" just means a lot of counters, like Delver has, rather than specifically a controlling strategy.
If you're dead-set on 1x Lotus 2x Mox being your only artifacts, I wouldn't run Tinker.
This is still very much a work in progress, but what I'm trying to brew is something to abuse Narset. Between Preordain, Ponder, Brainstorm, and 3 top, in my limited gold-fishing thus far, I've never +1'd Narset and
not drawn the card.
Instant (21)
1x Ancestral Recall
1x Brainstorm
2x Dig Through Time
4x Force of Will
1x Hurkyl's Recall
3x Lightning Bolt
3x Mental Misstep
1x Mystical Tutor
3x Spell Pierce
1x Swords to Plowshares
1x Wear
Sorcery (9)
1x Merchant Scroll
1x Ponder
4x Preordain
1x Time Walk
1x Tinker
1x Treasure Cruise
Planeswalker (3)
3x Narset Transcendent
Creature (5)
1x Inkwell Leviathan
4x Monastery Mentor
Artifact (7)
1x Black Lotus
1x Mox Pearl
1x Mox Sapphire
3x Sensei's Divining Top
1x Sol Ring
Land (15)
3x Flooded Strand
2x Island
1x Library of Alexandria
1x Plains
3x Scalding Tarn
3x Tundra
2x Volcanic Island