Why you should trust me and this build
Been playing [Gauss] since he came out and has a massive amount of my playtime (~73%). I have been toying with many different builds and this is the one that stuck. My go-to warframe for almost everything with a few exceptions.

Disclamer: Yes I play other frames, it just happens to be that I play [Gauss] too much.

Gloom is mostly here for the lifesteal and CC, the trade off is being totally reliant on weaponry.

So, let's get this out of the way the [Umbral Vitality] is replaceable to save umbral forma. I have played [Gauss] enough and feel like he is worth an umbra but if you're not comfortable with using an umbra forma on [Gauss] go right ahead and replace the umbral mod with normal one. Please keep in mind that your health and power strength will be lower. [Umbral Intensify] is not replaceable.

The Archon shards should be all crimson shards. Two on power strength for up to 240% strength with molt augmented ramped up and the other three on duration for an extra 45% and a total of 299.5% duration. All of these numbers are assuming tauforged shards.

With all of that out of the way, I can finally explain the mods.

Duration

By far the most important stat on [Gauss], duration boosts his entire kit in a way like no other frame as it almost acts like power strength should. That being said, [Primed Continuity], [Narrow Minded] and [Constitution] are fine, trust me. 306% duration isn't worth the slot. That and we get 300% duration due to archon shards anyway.

Efficiency

Untouched.

Range

Due to gloom being used at close range anyway for melee life steal, 124% is enough. You're trying to slow the enemies in your immediate vicinity, not the whole map. No need to waste energy slowing enemies that don't need to be slowed.

Strength

With 240% strength (Including molt augmented) gloom has roughly 84% slow and 12% lifesteal, good enough.

Full setup

Primary
Secondary
Melee