I contacted two professors six weeks before the deadline. One prof emailed me back immediately. The second one still hasn’t. It is due in 3 weeks. I emailed him last Friday asking him again if he would be willing to be a reference but still no response. I don’t have his phone number and he doesn’t work at the university. I really don’t want to annoy him, but should I email him again? I do have his gmail address (I’ve been emailing him from his work one). Usually he contacts me from his work one but I have received ones from his gmail account in the past. But I am afraid this would be frowned upon and looked on as being too invasive? I am really at a loss. I do have another reference, however, she is more a professional reference and I am not sure if that is allowed (the school isn’t getting back to me on this question).
This question is not a duplicate. I am wondering if I should email the professor for a third time or if that would be considered inappropriate?