MTG Salvation

I'm making a Traxos artifact deck and am confused. Can I play cards like Coveted Jewel or Vexing Puzzlebox and use their abilities to tap to add mana even though they want me to add mana of the colored types being black, blue, red, green, or white while my commander doesn't have those colors in it's identity?

I already learned I couldn't play cards like Gauntlet of Power because it requires you to choose a color, but that color can't be colorless. Realizing this is why I'm confused about the interaction with Coveted Jewel and Puzzelbox with a fully colorless deck.

There is no rule anymore preventing you from adding mana outside your commander's color identity. You can run Coveted Jewel in any deck and tap it for any color. This changed a long time ago. You may also run Puzzlebox in any deck, even colorless.
You absolutely can play Gauntlet of Power in any commander deck, and choose any color, no matter the color identity of your commander. You can't choose colorless, but that's because colorless is not a color, not because of any special Commander rules.
The color identity of your commander limits what the color identity of the cards in your decklist are. This counts mana symbols and color indicators anywhere on the card, but does not count color words, "choose a color" or "any color."

Ok, cool. Thanks!