I believe in Texas uses a terminology of signal or indication device in a courtroom.
Texas Transportation Code § 545.104
(a) An operator shall use the signal authorized by Section 545.106 to indicate an intention to turn, change lanes, or start from a parked position. (b) An operator intending to turn a vehicle right or left shall signal continuously for ...
In england-and-wales there is no legal requirement per se to use an indicator when turning in the situation described (but here it will be a right, not left, turn).
Rule 179 of the Highway Code states that:
before you turn right you should ... give a right-turn signal
The Wording of the Highway Code states that the use of should makes this an advisory ...
The Ohio Court of Appeals has addressed a nearly identical situation in State v. Paseka.
The relevant law is, as you noted in the question, R.C. 4511.39, which states, in relevant part:
No person shall turn a vehicle or trackless trolley or move right or left upon a highway ... without giving an appropriate signal
The facts in this case are ...