Should that be placed here:
On 12/10 the physician notes indicated that on evaluation the patient had a poor oral intake and her pain was not well controlled on Tylenol alone.
or here:
On 12/10 the physician notes indicated [no pronouns] on evaluation that the patient had a poor oral intake and her pain was not well controlled on Tylenol alone.
That in this sentence is not, as you appear to think, a relative pronoun but a subordinating conjunction (in traditional terminology) or subordinator (in modern terminology). It 'marks' the following clause as subordinate: in this case the Direct Object of the verb indicate.
So this is really more a question of where the phrase on evaluation is placed, before or after the subordinator that.
That phrase is a time reference modifying the clause it is placed in.
If it is placed before the that, it belongs to the main clause and modifies that, telling the reader when the notes 'indicated' the patient's symptoms. That is absurd: the notes 'indicate' the patient's symptoms whenever they are read, not just at the time when the patient was evaluated.
The phrase therefore belongs after the that, so that it is belongs to the subordinate clause and tells the reader when the patient had these symptoms and complaints.
