A cap won't work; it would be the size of the radio to store enough power to run the radio for a few seconds.
What you want is a capacitor that holds a RELAY on, and let the relay feed the "switched" power to the radio. The relay draws far less, so it will run longer on a reasonably-sized cap.
The cap needs to be isolated from the truck by a diode so it's not powering everything else on that ig.sw. feed. The relay's main input needs to be either fused, or fed by the original fused radio power circuit (137 Y/Bk).
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But an easier, cheaper, & more-reliable solution (IMO) would be to use a common SPDT (Bosch/ISO/Tyco) relay. Trigger it from the ig.sw. "I" output (904 Gn/R, 640 R/Y, 932 Bu to terminal 85; terminal 86 to ground) so that it switches its output (terminal 30 to the radio switched power input) between the original radio wire (137 Y/Bk on terminal 87a) and a new fused UNswitched battery feed (on terminal 87). No capacitor needed, and the radio will stay on except when the key is in OFF. Here's what would happen in each key position:
ACCY - radio powered only by the original switched feed thru the relay's NC contacts
OFF - radio off
RUN - radio power is switched by the relay from the original to the new feed
START - radio powered only by the new feed, uninterrupted during cranking