Language is amodal, which means:
"The human brain does not discriminate between the hands and the tongue. People discriminate, but not our biological human brain." -- Dr. Laura-Ann Petitto (Gallaudet Today, Spring 2012, p. 17)
"Language is not mouth stuff – it’s brain stuff.” – Dr. William Stokoe, the father of ASL linguistics.
This Gallaudet's video below explains all important information in short on the brain, language, modality (signing and speech), language acquisition, and myths and facts on cochlear implants.
"Sign language is the equal of speech, lending itself equally to the rigorous and the poetic, to philosophical analysis or to making love." -- Oliver Sacks.
Emmorey, K., & McCullough, S. (2008). "The bimodal bilingual brain: Effects of sign language experience", Brain and Language , doi:10.1016/j.bandl.2008.03.005
Karen Emmorey. "Sign Language and the Brain". Language, Cognition, and the Brain: Insights From Sign Language Research. Chapter 9: pp 271-314.
Lane, Harlan, et al. (1996) A Journey into the Deaf-World. DawnSignPress. Pp 101-104.
Petitto, Dr. Laura Ann. Untitled. Montreal: McGill University media. October 28, 1997.
Newman, A.J., Bavelier, D., Corina, D., Jezzard, P. and Neville, H.J. A critical period for right hemisphere recruitment in American Sign Language processing. Nature Neuroscience, 5:76-80, 2002.
Szwed, Marcin, et al. (2017). "Whether the hearing brain hears it or the deaf brain sees it, it's just the same." July 21, 2017. https://www.pnas.org/content/114/31/8135
You may also be be interested in bilingualism and bimodalism.
Sr William Stokoe: the father of ASL linguistics.