How to clone and sequence a gene transcript of unknown sequence?
Perhaps you can draw inspiration from classic paper on lambda cloning:  Maniatis T, Hardison RC, Lacy E, Lauer J, O’Connell C, Quon D, Sim GK, Efstratiadis A. 1978. The isolation of structural genes from libraries of eucaryotic DNA. Cell 15: 687–701.

Try selecting tissues from the animal which you think is "enriched" (i.e. highly expressed) for the specific gene you're looking for. This might take a little bit of guessing. For example, if gene A is very highly expressed in tissue B, then you can "assume" most of the mRNA transcripts will be for that of gene A. Do a RNA purification, RT-PCR, and clone the cDNA into lambda vectors and pick plaques. With a little bit of luck, you'll be able to identify the gene by cloning, hybridisation, and subsequent chromosome "walking" to determine it's structural origin.

This was done back in the day to identify novel genes way before genomics, sequencing, or even PCR!