In the state of Utah, if a person runs a red light and receives a citation for causing the accident can the other party involved in the accident be found partially liable by the first party's insurance agent?
Normally if a party runs a red light, they are almost always going to be 100% at fault. You mention that the red-light runner's insurance agent is "finding" you partially liable for causing the accident. Keep in mind, the adjustor or agent does not hold any legal authority for determining who was at fault. They are acting in the best interests of their insured, not you or the public. So, if they are taking an unreasonable or not legally valid position, contact a lawyer for help and advice.
As I am licensed in Florida and Vermont, I cannot offer you specific legal advice as to Utah state law. However, an insurance company will claim or say almost anything to avoid full payment on a claim.
You are not obligated to provide the adverse insurance carrier with any statement and I would advise you against providing a statement, as they will attempt to use it against you to find you somehow comparatively negligent in contributing to the collision. An "insurance agent" does not determined liability, a jury does.
Generally a person running a red light would be at fault, although there could be contributing circumstances from the other party, such as excessive speed, which could be deemed comparative negligence which contributed to the collision.
Fault, in personal injury cases, determines liability for an accident. Someone who is found at fault may be required to compensate the victim through damages.
There are many types of personal injuries for which financial damages can be awarded, including physical, emotional, and psychological injuries.