I want to play a Hexblade Tomelock with a shield and rod without the War Caster feat. And I want to shoot sparklies out of my rod.
I understand the general rules of components and the examples of wizard & a cleric given in sage advice.
What I don't have neatly put together is this series of tweets by Mr. Crawford.
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This one makes it seem that a hand with a focus is free when a spell requires only somatic (no material) components.
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In this one, Mr. Crawford seems to make a distinction between a holy symbol (or other focus) and a symbol emblazoned on a shield.
So, can a Hexblade Warlock use one hand hold a shield, the other a rod, and still cast Eldritch Blast?
Best Answer
You ask in the title: What's the mechanical difference (as related to somatic components) between a holy symbol on a donned shield and a focus held in the hand?
Answer: From the point of view of spellcasting, there is no difference.
(The shield has the non-spell-related advantage of providing a bonus to your AC, but can only be used as a focus by clerics & paladins.)
You ask at the end of your explanation: can a Hexblade Warlock use one hand hold a shield, the other a rod, and still cast Eldritch Blast?
Answer: You have it right there in your own background info.
The Sage Advice page that you linked says:
Eldritch Blast has no Material Component, so you'll need a free hand to make the somatic gestures. You'll have to put down either the shield or the rod.