Im not a doctor, so i have no idea what the cause of your problem is but there are plenty of scenarios that I can think of.
Alcohol is a CNS depressant so it will effect your heart rate to a degree if all you are doing is sitting and drinking.
But the heart is also self excitatory, so it will continue to beat regardless, unless it goes into defibrilation etc...
Your resting blood pressure and heart rate is pretty decent so thats good. The only thing i can think of is that your circulatory system seems to be quite efficient when your resting. Then when you start drinking, this depresses the activity of the CNS and you perhaps get a slow down in CNS stimulation of the processes that normally occur in the body. When those processes slow down, you wont require as much energy to maintain homeostasis. Oxygen is required to make energy and because you dont need as much energy, you dont need as much oxygen transported. So the way your body deals with that is to slow your heart rate etc.
Or, when you drink your body is trying to process the alcohol so it constricts your blood supply to your arms and legs to a degree (which is where you will be measuring your pulse/BP i would expect) because its sending all the blood to your stomach to absorb the alcohol and transport it to your liver.
How tall are you?