I was making a Gadgeteer character and was wondering if I could

IMO, that was written in such a way as to intentionally provoke a discussion between you and your GM. Each game may choose to answer that question in a different way, depending on the people involved.

But for me personally, I don’t see anything in the description that requires the jury-rigged device actually belong to you — it just has to remain “in use”, which I assume means that the jury rigged nature requires frequent maintenance by someone who is capable of doing so. You don’t necessarily have to be the one to continue to maintain the jury rig in place, but the jury rig does require that someone continue to maintain it.

No. It says a personal piece of equipment. Tinkerer is a little more open ended. Coulda swore the Jury Rigged question was asked and answered by the devs.

"The character chooses one personal weapon or piece of armor....The bonus only applies so long as the character is using the item. If the item is ever lost or destroyed, the character may apply Jury Rigged to a new personal weapon or piece of armor."

IMO, I would rule that the benefits of the Jury Rigged talent are non-transferable. It sounds as though that if I applied this to my blaster' damage and handed it to another PC, he/she would not gain its benefit. The talent represents the temperamental and semi-permanent tweaking of equipment by an incessant tinkerer.

If I were to allow the benefits to be transferable, the talent would still only apply to a particular PC. This would prevent a PC from making an arsenal of jury rigged blasters that can be handed out to anyone. If you want permanent upgrades, buy attachments.

No. It says a personal piece of equipment. Tinkerer is a little more open ended. Coulda swore the Jury Rigged question was asked and answered by the devs.

I would say in this case I think personal refers to scale rather than possession, but I agree with you.

From E-CRB, page 138:

JURY RIGGED
Activation: Passive
Ranked: Yes
Trees: Gadgeteer, Outlaw Tech

The character chooses one personal weapon or piece of armor per rank of Jury Rigged. He may increase the damage of the weapon by one; decrease the Advantage cost on its Critical, or any other single effect by one to a minimum of one; or increase [the] armor’s ranged or melee defense by one. Alternatively, he can decrease the encumbrance of the item by two to a minimum of one. The bonus only applies so long as the character is using the item. If the item is ever lost or destroyed, the character may apply Jury Rigged to a new personal weapon or piece or [of] armor.

So, I was wrong. Only so long as they keep ownership and possession of the item in question, can Jury Rigged be applied to it.

My bad.

[EDIT: Fix the color of the title for “Jury Rigged”, since it doesn’t show up as well on a different background.]

Can Jury Rigged be applied to the same weapon or piece of armor more than once?

Can Jury Rigged be applied to the same weapon or piece of armor more than once?

No. Each rank of Jury Rigged affects a different item. "The character chooses one personal weapon or piece of armor per rank of Jury Rigged"....not one modification to one weapon or armor per rank.