How long should I give ex space?

My girlfriend dumped me back in April. She gave me a couple chances at proving to her I wasn't clingy and needy, but messed up every time. 3 weeks ago she called it quits "for good" and left for her annual Denmark trip. Throughout the trip, she has been hot and cold. Some days she will send a random feeler message like "how are you?" Or "hey.." Or even start a conversation. Sometimes we even video chat for an hour plus. We laugh and even reminisce about memories together. But as soon as I bring up dating or even hanging out She becomes cold. Gets angry saying "I wish you would drop it" Or "I wish you would get any glimmer of hope out of your head." Or "I'm not giving you another chance. You just can't change." Or "You just don't get it." Usually when she becomes cold I say I understand her anger and explain why politely. ("I was clingy in the past and I don't blame you for being hesitant now etc etc.") Since she's been gone, I've been seeing a therapist to tackle my insecurity. Also been working out (lost 29 pounds) to gain confidence. At one point, she tried lying to me saying "I've found someone else." She later admitted she lied because "she wanted me to lose hope." Last time we video chatted she claimed once again she had someone else and I'll find out soon enough who it is. I really don't want to believe she's moved on already even though she claims she has. She's been hot and cold. When she's hot it's like we are dating again. When she's cold she's just plain barbaric. This morning I sent her an "elephant in the room text" basically apologizing for my past mistakes, acknowledging the breakup happened, and how I have improved since then. I then told her to take a few days of space to let this sink in, and when she returns we can talk. If after the talk she wants to block me forever, I won't argue. If she wants to see where it leads, we go from there. She read it and never responded. Should I wait the 5 days until she gets back to attempt to contact her again?
How long should I give ex space?
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