Help with Starter Interrupt

I installed an OEM Ford System 6 alarm/remote entry system on a 94 Ford Explorer with manual transmission.  Per the installation instructions that came with the system, I wired the starter interrupt wires from the system (without a separate relay, per instructions) in series with the starter wire at the steering column.  When testing, the alarm box emits a buzzing noise whenever I push in the clutch.  This sounds like a relay cycling and gets worse when the engine is running.

The clutch on this vehicle has a switch which interrupts power to the starter circuit when the clutch is engaged (not pushed in) and provides continuity on that circuit when the clutch is disengaged (pushed in).

To allow the vehicle to be driven, I disconnected the interrupt from the system and jumpered the wires-- there is no buzzing now, but obviously the interrupt is not functional.

I'd appreciate any advice you have on solving this problem.  I'd like to avoid installing an extra relay if possible, but if this sounds like an overload of the system's relay, please let me know.

Thanks in advance for your help!

The clutch was not bypassed (this is not an automatic tranny)-- the clutch switch is wired in series with the interrupt on the starter wire. 

Thank you for the suggestion, I'll give that a try!