Regarding bIQ SeH jan, a suggested way to refer to a "faucet" -

Maltz says this is really two words: bIQ SeHjan ("water control-device" or "water controlling-device").

The question, based on the three-word version, was whether the suffix -meH, following SeH, was missing or deleted or could be added. And a followup question was, if so, could other similar phrases be formed by simply dropping -meH.

Speaking historically or etymologically, a formation such as bIQ SeHjan was no doubt formed by reducing the phrase bIQ SeHmeH jan ("device for controlling water") by dropping the -meH. And, still speaking historically or etymologically, this could happen again for other words.  It is not, however, a productive process - that is, you can't, on the fly, just drop the -meH. In everyday conversation, people may do this anyway, and some other constructions may well have come about this way (or may come about this way in the future), but, except for the set, accepted expressions (which, of course, may increase in number as time goes along and speakers accept newer formations), dropping the -meH is considered odd.

So does the existence of SeHjan imply that there's a noun SeH (meaning "control" or "controller") that exists alongside the verb SeH (meaning "control")? There may be such a noun, but, if so, Maltz says he's never heard it used. He said the SeH in SeHjan and SeHlaw ("control panel") and 'eDSeHcha ("take-off/landing thrusters") and elsewhere is clearly related to the verb SeH, but using SeH (a noun) as an independent word felt weird to him. But he's changed his mind before…

Having said all of that, referring to a faucet as bIQ SeHmeH jan is fine. And the original three-word phrase that led to the confusion, bIQ SeH jan, is a well-constructed sentence meaning "the device controls the water."