AIUI, BCM4365 is the model number and ID of your hybrid wifi/bluetooth device, whereas BCM43142 is the model number of the wifi device within it.
It appears BCM43142 is supported in the latest broadcom wl driver. whether the device is supported in our current wl extension you will have to try it to find out, but my money is with this solution.
Should I add wl-modules-4.2.9-tinycore64.tcz to /mnt/sda1/tce/optional?
not if you're only booting tinycore 32bit
you should use APPS to add these extensions to onboot listGotTo: APPS > Maintenance > OnBoot Maintenance
to the list.
Note: remove any other wifi related extensions accidentally added previously to this list
wifi dependencies will be loaded automatically when wifi.tcz is loaded (if deps are installed to tce/optional)
you will need to blacklist the original broadcom modules, add this to the boot config file
MENU LABEL TinyCore
APPEND initrd=/tce/boot/rootfs.gz,/tce/boot/modules.gz loglevel=3 tce=sda2 opt=sda2 home=sda2 blacklist=bcma,ssb,b43
note any error messages
You may nee to enclose your SSID with "" as mentioned below.
if unable to connect post the dmesg again