When going on a Singing audition, your portfolio and resume most likely got you in the door. If you have a Singing agent, that agency will put together your portfolio and promote you to companies looking for new faces for their product. Depending on the product being sold, different jobs will require different looks.
When creating your portfolio, try to include pictures that showcase the different looks you might have. Never be too bold if you can pull it off. The more options you may be able to display as a model, the better chance you have of booking a job. Most models have a look or genre they are most confident with, so stay true to what you think your best look or style is.
On a Singing audition you will be brought in to meet with the casting director or producer of the project being cast for. They may take some test shots of you and meet with you briefly, but there is nothing more to prove than the right look. Models don't necessarily have to "act" if the look is right.
When you go to the audition, bring your portfolio along with a headshot or card along with your measurements. All models should have available their height, weight, shoe size, hat size and waist. For males, you should know your suit size, shirt size and inseam. For women, you should have available your bust size, hips, dress size, blouse size and pant size.
Be courteous, polite and most important, be yourself on a modeling audition. You are not necessarily acting a part, but selling your look. A polite and professional attitude will only help your chances. If a casting director doesn't like your attitude, they may never higher you again.