The simplest way to avoid being mistaken for an American citizen is simply not to declare war on their country. And the easiest way to convince them you are Australian is simply to avoid acting like an American - but just a side note, it may involve smiling, being nice occassionally, and at least attempting to speak their language. Native Jordanians are considerate people who enjoy conversing with tourists during lunch and dinner - but beware, they may converse for a little too long and expect you to pay for their drinks. During occassions where politicians and famous visitors enter the country, security is usually heightened. Tanks and armoured vehicles are simply a precaution against terrorism. On any normal day the military presence is halved, and their spare time is used up by taking pot shots at young children begging on the street.
Actually that last bit isnt entirely true. All Jordanians were extreamely nice while I was there and I recommend visiting the country - even if American. Actually I met some very nice Americans in Jordan so dont fall for the common mistake that American people have the same opinions as their President and his crazy staff.