So you want to open a drop down select box without clicking on it? For years, people have been looking for the answer to this question. While everything else on the web has been changing since, the answer to this question remains the same.
Instead of wasting your time let me solidly state this for you…
Solid Tip: You cannot open a select element with a script.
What are my alternatives?
Sorry to burst your bubble back there, but it’s not possible. Better men than me have tried and failed.
This basically means you make a div with an arrow graphic, add a click event to it, then pop open a box onclick that shows a stack of option divs. While it is certainly no small task, it will allow you to add any number of features that would not be possible in a normal select element like opening it using scripts or styling with full CSS support.
At least you won’t have to continue your wild goose chase looking for something that can’t be done.