I should like to suggest reading anything and everything you can get a hold of on the subject. Make some things you find interesting. For example, a set of surface plates or straight edges using Whitworth's method, a Kelvin-Varley divider,a Michelson interferometer, a Lacoste-Romberg gravimeter. The list is endless and what you choose doesn't matter. The objective is to understand the logic of metrology. How do you *know* that is a straight line? What are the limitations and errors?
Learn the history of metrology. Who developed what, when and why? If you read 8-12 hrs a week you'll get there pretty quickly. If you encounter stuff you don't understand, skip over it and keep going. Come back to it later. I took a job right after finishing my MS in geology as a geophysicist. I knew absolutely *nothing* about reflection seismology and digital signal processing. I spent my evenings and weekends poring through a stack of books. When I got to the bottom of the stack, I started over. Very quickly I began to understand everything I read.
Make a point of reading all the professional papers published by the national metrology laboratory where you live. When you think you understand the papers, contact them asking questions that show that you've read the paper closely. For example, why did you choose this approach rather than the method in the paper by so and so? Such a question should be focused on something they glossed over or better yet, didn't state. What method did you use for such and such? Just don't fake anything. You'll be spotted in a heartbeat and your chance will evaporate in an instant. Once you have their attention ask it they have an intern program.
If you get to where you can carry on casual conversation with a metrologist of any type that demonstrates you understand what they do, what the issues and problems are and so forth you'll get a job. You do not need to be an expert on anything. What I'm describing is the sort of conversation a couple of people from different sections of a metrology lab would have in the cafeteria over lunch.
Most of all,
Have Fun!