>It is also possible that . . . lens . . . contact is intermittent.
Ah, yes. This is also a strong candidate, thank you. As you say, the low voltage may be impeded by mind-bendingly small amounts of corrosion or dirt but, once re-established, the path will tend to remain open. This nearly fits the situation, but fails to explain the successful acquisition of focus by auto-focus prior to the shutter hesitation. (In this instance, AF-C removes all consideration of focus achieved or not.) Presumably such a fault would interfere with the actuation of the focusing motor and make itself known by that association. (BTW, I misspoke, the Tamron has an internal motor but resists hand turning - unlike AF-S lenses - with much the same gusto as a camera drive AF lens.) But, short of setting the camera to MF, I suspect an intermittent bad connection with the lens could indeed make itself known in this manner if it is torn between acting as a valid circuit or an open switch.
I need hardly mention that whatever the problem may be, it is currently in hiding. No doubt the camera heard us talking about it. It doesn't seem to be in the act of changing lenses since the camera has had several different lenses on it in the past few days with no complaint.