This feature might well have been added by a PO due to the nature of the S1 fan control. The AC knob left of the radio controls an adjustable Ranco thermostatic switch. At full left, the power to the compressor clutch is off. When the switch is advanced to the right, a thermostat sensing the evaporator coil temperature turns the clutch on until the the set temperature is reached, then turns the clutch off. In operation, the clutch cycles on and off. The fan control switch is (mostly; see below) independent and used for both AC and heat.
By 1971 at least, Jaguar fitted a microswitch to the Ranco switch that operated from a cam attached to the switch’s shaft. The microswitch was in parallel to the “low” setting of the fascia-mounted two-speed fan switch. This assured that at least the low fan speed was switched on whenever the AC compressor was powered (Ranco switch advanced past “off” position). The reason was to prevent evaporator freeze up which could occur if the AC was in operation with no air blowing through the evaporator.
But on a cool day, even if the thermostatic switch is not fully rotated to the left (off position) the compressor will not cycle on, so a driver might not bother to ensure that the AC is off. In this case, the fan will be on even though there is no AC and even though the fascia switch says the fan is off–this might be why the warning light was fitted. It’s also possible that the light is wired to show AC clutch cycling–an excellent way to check on AC operation. In your testing, the fan being on might be merely a concomitant of the compressor clutch being engaged.
BTW, in 1972 the circuit was changed so that the Ranco switch by itself selected a fan speed that is slower than “low” set by the fascia switch. So, in AC mode but not heat mode, there are three fan speeds available.