What type of Bacterial infection was it that Lincoln had last year? It's odd that they have a strictly topical infection in one, isolated area unless they have an open-wound that becomes infected, or they have an infected feather-follicle...Did the CAV tell you last year what type of infection it was, or what was causing it or why it happened? Meaning did Lincoln have a cut/wound in the area prior to it becoming infected, or was it a feather-follicle that was actually infected, or was it just an area that Lincoln often picks at or plucks and that's why it got infected?
If Lincoln had/has a systemic infection or an infection of his mouth/sinuses etc. and he picks only one single, solitary area on his body, then it's possible that this specific area could become infected if he breaks the skin open or he pulls the feather out and digs at the follicle...However, that's highly unlikely because if he had some type of systemic infection in his mouth/sinuses/throat etc., then he would have also had other symptoms, i.e. he would have been actually "sick" instead of just having a topical infection on the back of the neck...So it's difficult to really say what's going on without knowing what was actually diagnosed the first time this happened...Although if the Vet only did a skin swab last year and diagnosed only a topical infection, it's hard to really say what was going on anyway.
Was Lincoln given a topical antibiotic that you applied to the area on the back of his neck, or was he given a systemic antibiotic, like one you gave him orally? Because if it was an oral antibiotic and it cleared-up the topical infection on the back of his neck, then something else was most-likely at play...
***I'd say that if Lincoln is developing another infection or is picking/plucking at exactly the same spot as he was last year, then something else is going on and you need to talk to your CAV about doing some different diagnostic testing besides just a swab of the topical wound/infected area. He should probably have a Fecal Culture/Microscopy done, along with a mouth/throat swab, and if he hasn't yet had routine Blood-Work done this year, then now is the time to get it done, all at once while you have him there at the Vet's office. It's very odd that the exact same spot on the back of his neck keeps bothering him enough that he's picked at it and it's gotten infected two years in a row...I haven't seen the area but sometimes they get Cysts of their feather-follicles, and they will not ever go away unless they are drained and the Cyst-sac is removed...But, they can become infected over and over again, so it's possible that Lincoln has a Cyst in that area (or other Dermal mass, like a Dermoid/Pilar Cyst, a Lipoma, a Granuloma, etc.) and it keeps becoming infected...If that's the case it will just keep becoming infected/inflamed and then the infection would keep clearing-up with the Antibiotics, but the Cyst/mass itself will still remain unless it's removed...So that's one possibility. I don't know if you can visibly see any type of lump in the area or feel any type of lump in the area under the skin, as sometimes they are deep and you can't see them, but if Lincoln will let you I would gently palpate the area that is bothering him and see if you can feel any type of lump or similar under the skin in the area...If you do, then that's your answer. That would explain the exact same area continually flaring-up and becoming infected over and over again...In that case the Vet would simply drain the contents of the Cyst (if possible) and then cut-out/remove the Cyst sac so it won't return again, and probably send the sac off for pathology to make sure it's nothing malignant, which 99% of the time Cysts, Lipomas, etc. are not.
Otherwise, if it's not a Cyst, Lipoma, or other mass under the skin that keeps getting infected and needs to be removed, then it could be a single Feather-Follicle that isn't producing feathers normally or that is malformed and is causing the feather shafts to grow-in "wonky", for a lack of a better way of saying it, and these bother Lincoln as they grow-in, so he starts picking at them, and that causes them to become infected. I've seen this happen many times, and the solution to this is to remove the culprit feather-follicle. Sometimes they just don't work properly for whatever reason, and whenever they produce a feather they grow-in improperly and they bother the bird, just like an in-grown hair bothers us. The only difference is that feathers have hard shafts, and when they grow-in the wrong way they can actually cause a lot of discomfort to the bird, which causes them to try to pull or dig them out, and they become infected. That's another common possibility...
Otherwise, maybe it's just an area on Lincoln that for whatever reason becomes very dried out and itchy, which causes him to dig and pick at it, which results in the area becoming infected. I would definitely make sure that your Vet examines the area very closely and palpates it closely to rule-out any type of cyst/growth or abnormal feather-follicle before he just goes right to "He picked at his skin in this area again and that caused a topical infection", because cysts, lipomas, granulomas, and abnormal feather follicles are extremely common in birds, just like the same types of growths and problems are common for us in areas where hair grows. So you definitely want to rule-out any underlying issue before just going to "Here's an antibiotic"...