Should I push, pull or wait?

I hope someone can help me with this. I broke up with GF 1 1/2 months ago. Basically she dumped me for getting drunk and acting like a fool on her BDay. She cut all contact for a few days, then said she wanted sompe space and all that crap. She had warned me several times on my drinking I said I would stop that week (my sis was getting married). But she didnt go to the wedding the day after and didn't even callme or answer my calls.
Now after some time we talk from time to time. A couple days ago we had a long text conversation on fb, yes I was drunk, and I think I made a big mistake. I asked her what if I quit drinking (for some time) and we make a clean start again. She replied If that was the case I would be willing to come back; That if I do that It would be a great thing and she would be happy. But deep inside she doesn't believe me I think. I know I can do it I've done it before. I also know this is not an aa forum lol.
So she then said (cause she noticed I was drunk while texting her) But if you lie to me ill notice. I said "how would you notice?"

She- " Well I could ask for off days at my job and stay with you from wednesday to tuesday or somthing like that. But call me tomorrow at 11 am whern you're sober and tell me this again...

Well, the thing is I don't want to get back on her terms or having a cop nugging me. So Next day I sent a quick message at 9 o clock sayng good morning slob. she replied like around 12 am saying "slob? I woke up at 7:30 AM got into my car and headed to the beach. I answered 2 hours later. we exchanged a couple messages afterwards and I called her at night but her phone seemed to be off or something. I sent her a message saying I called you and as I suspected you didn't answer whow was the beach...etc.." Nothing serious. Next day morning she sent me a message saying she didn't get my call, but I messaged her eraly and then never messaged or called again.
I'm sorry for all the details I know you don't want to get all the bs.
So I just sent her a message about 2 hours after that teasing her about a pic she posted. that was monday. Now it's wednesday night, haven't contacted her at all.

Now what would you think...after spilling the words "start again" to which she said she would be willing to do it if i control my drinking... Do you think this is a step forward from before when she "needed space". Did I blow it? Should I make a strong push now after saying those words (take in mind I was drunk and she knew it but I didn't call next day to reconfirm). Or should I keep talking to her, or wait till she contacts me and stay aloof (while I hit the gym and detox a bit by the way).

So push, Pull, or wait?

By the way I do have an alcohol problem but it is not that serious. In fact i had quitted before I farked up at her bday. Well at least now I know the reason why she dumped me (It was kind of obvious though).

Thanks for reading what do you suggest? And no, "quit drinking" advise won't help me, I already know that I have to do that.

The thing is...should I call her and tell her that again as she asked? I haven't done that yet. I don't want to get back on her terms.

Advice much appreciated.

First stop apologizing so much to us or anyone else, you're here for advice so it's ok

Second yes your drinking will need to be something you can get under your terms, work on it. I used to drink too much too, I understand it may not be an addiction but the habit needs to be broken still. Don't bring it up again, when she does you can address it like that - this is something I'm trying to balance with myself, etc etc, so it's not so much like you want her to police you

third she said ok shes willing to give it a shot, If you push too much you may overwhelm her so step back slightly but maintain contact. You wanna be funny and cool and make her curious about you again without being overbearing. Yea a little Push Pull, but in general spacing out your texts, waiting period, etc, all good stuff

Keep communication, don't lay it out to her again, just communicate like you would if everything was already going great, light and funny, not everyday, some inconsistency is good

Thanks. In fact she called me today after almost 2 months....so I guess I'm not doing it so bad. Cheers.