Does the Mechromancer's 'Electrical Burn' skill also cause burn damage effects from other skill-based shock/electrocute status damage effects?

I'm currrently planning out my Mechromancer's Little Big Trouble skill tree build.

I would like to know if the Mechromancer's Electrical Burn skill also work with shock/electrocute status damage effects from other skills? (i.e. Shock Storm, Shock and "AAAGGGGHHH!", One Two Boom and Make it Sparkle [Deathtrap charged with a shock/electrocute weapon]) Will those skills also cause Electrical Burn to give a chance that enemies will burst into flames and take Burn damage? Or does Electrical Burn only work with shock/electrocute damage from guns?

Skill effect descriptions from Borderlands wikia:

Electrical Burn

When your Electrocute Status Effects deal damage to enemies, there is a chance they will burst into flames and take Burn Damage. The amount of Burn Damage is based on the Electrocute damage dealt.

Shock Storm

Killing an enemy with a Critical Hit causes an Electric Storm, dealing Electrocute Damage to nearby enemies. Electrical Storms are also caused by Deathtrap whenever he kills an enemy.

Shock and "AAAGGGGHHH!"

Reloading your gun causes an Electrical Explosion, damaging nearby enemies.

One Two Boom

Deathtrap Ability. Deathtrap shoots out an orb of energy at an enemy. If you shoot the orb it will explode, dealing massive Shock Damage to nearby enemies.

Make it Sparkle

Shooting Deathtrap with an elemental weapon charges him with that element, causing his melee attacks to deal additional damage of that element.

EDIT: There is now an answer that explains how this works generally. Can anyone with experience on using the mentioned skills, comment or answer on which specific skills 'Electrical Burn' will cause burn damage effects with?

Solution 1:

Yes and no. As I eluded to in the comments, this takes effect only with "electrocute" Damage Over Time effects. Whether or not they're a result of your skills or guns doesn't matter, it just has to be electric DOT caused by you (deathtrap counts as you).

How it really works is every time an enemy takes electrocute Damage Over Time, there's a chance they'll catch fire, too. It never seems to start upon the initial hit with a Shock attack, and it can happen if you stop shooting but let the enemy fry for a second. Most of Gaige's electrical skills will induce Damage Over Time, so many of them have a chance to burn as well.

Solution 2:

According to tests done by user Zikel (originally posted at the /r/Borderlands subreddit), Shock Storm can activate Electrical burn even if created by Deathtrap.