I've heard that if you shine a strong light through your sac and see it on the other side then it is a hydrocele. Is this accurate?

Transillumination. Bright light shining through a scrotal swelling usually means that a hydrocele is present, however transillumination also occurs if there is a testicular tumor in addition to the hydrocele. Thus not a completely reliable sign and does not replace accuracy of scrotal ultrasound.
Perhaps. In general, hydroceles will "transilluminate" and this test helps with the diagnosis. It is not foolproof and since hydroceles can also occur with other pathologies it needs to be assessed by a urologist. Scrotal ultrasound is a far more accurate means of confirming the diagnosis and ruling out other pathology.
No. Fluid (such as hydrocele fluid) transmits light whereas solid structures like a testis or a growth do not. You have a hydrocele if: 1. You have a scrotal mass 2. The mass transmits the light.