If an agent takes both email and written queries and doesn't specify a preference, would a five to ten second call to find out their preference be appropriate? I fear encountering a situation like you mentioned earlier in which an agent listed that they took e-queries, but didn't actually read them.
Please please please do not call to ask this.
Send an e-query.
If you don't hear back, send a written query unless the agent says they only read e-queries.
There is no such thing as a five second phone call.
I've gotten these calls. Almost inevitably the author is so nervous they sound like a junior high boy asking a girl to the dance OR , worse, emboldened by actualy getting Miss Snark upon the blower, they PITCH.
I fly solo which means I answer my own phone. I let you ring to voice mail if I know you're not on my call list today (ie your area code is Winnemuca). The ones that really chap my chatanooga choo choo are the ones that come in as "private caller" and I answer thinking it might be Mr Clooney. Or Grandmother Snark. Or the gin delivery truck driver needing bail money. And worse upon worse is when I've put someone else on hold to answer this and then you pitch. You're unhappy when I cut you off. I'm unhappy. My other caller is unhappy. This is not the start of something good.
I know this can seem like some sort of Byzantine world of nonsensical rules and crazy agents who don't want to talk to the very people who provide the work they sell. Pause for a moment and consider it only takes 1/10 of my queriers in any given week to add up to a lot of phone calls. We do this not cause we want to make it difficult for you but because we want to spend our time doing what you REALLY want us to be good at: selling stuff.
If worse comes to absolute worst, you can email to ask which is better. At least then Mr Clooney won't get a busy signal when he calls.