Back to the original thought; would the flush mount style of gauges akin to what's on the new SERKs work on the 02 when the P&A fitment description for the kit 62823-06A says otherwise? That kit gives a fitment of simply "04-07 Road King."
Compared schematics of pre and post 04 bikes. Specifically 02 in question and an 05. While termination points away from the gauge and sending unit for 12v supply vary between the accessory or the instrument circuit they still get fed. Common is, well; common. And the 05 has a T off the run between the sender and the gauge that the 02 does not. It feeds the low fuel idiot light in the speedometer. No impact on gauge function there either. Just a difference of there being an idiot light or not.
From all that, and fitment descriptions notwithstanding, it looks like it should work. Seemed to lean even further toward that when comparing other LED fuel gauges Harley offers. All the precedent offerings have a fitment description of:
"Fits '04-'08 FXDB, FXDL, FXD35, FXDWG and FXDF models, '07-'08 FXDC models, '04-'07 Softail® models, '01-'03 EFI Softail® models (except FXSTDI), '03-'07 Road King® and '01-'02 EFI Road King® models"
So at least for EFI bikes the LED gauges reach back as far as 01. Looked at the PDFs of a couple of their install docs and nothing different about the physical or electrical connections on any of them. Might later be proved wrong by something not being recognized but it seem so far as if this could be another case of P&A fitment descriptions not being accurate or not throwing as wide a net as they might.