Remove three sides of border around ggplot facet strip label - r

Question

I have the following graph:
And would like to make what I thought would be a very simple change: I would like to remove the top, right and bottom sides of the left facet label border lines.
How do I do I remove those lines, or draw the equivalent of the right hand lines? I would rather not muck about with grobs, if possible, but won't say no to any solution that works.
Graph code:
library(ggplot2)
library(dplyr)
library(forcats)
posthoc1 %>%
mutate(ordering = -as.numeric(Dataset) + Test.stat,
Species2 = fct_reorder(Species2, ordering, .desc = F)) %>%
ggplot(aes(x=Coef, y=Species2, reorder(Coef, Taxa), group=Species2, colour=Taxa)) +
geom_point(size=posthoc1$Test.stat*.25, show.legend = FALSE) +
ylab("") +
theme_classic(base_size = 20) +
facet_grid(Taxa~Dataset, scales = "free_y", space = "free_y", switch = "y") +
geom_vline(xintercept = 0) +
theme(axis.text.x=element_text(colour = "black"),
strip.placement = "outside",
strip.background.x=element_rect(color = NA, fill=NA),
strip.background.y=element_rect(color = "black", fill=NA)) +
coord_cartesian(clip = "off") +
scale_x_continuous(limits=NULL)
Data:
structure(list(Dataset = structure(c(1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 5L, 5L, 5L, 5L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L,
3L, 3L), .Label = c("All.habitat", "Aut.habitat", "Habitat.season",
"Lit.season", "Spr.habitat"), class = "factor"), Species = structure(c(1L,
2L, 3L, 5L, 6L, 10L, 11L, 12L, 13L, 1L, 3L, 5L, 6L, 13L, 1L,
2L, 5L, 6L, 7L, 8L, 9L, 10L, 11L, 13L), .Label = c("Ar.sp1",
"Ar.sp2", "Arc.sp1", "B.pus", "Dal.sp1.bumps", "Dip.unID", "I.palladium",
"Pale", "Ph.sp3", "Port", "Somethus", "sty", "Sty.sp1"), class = "factor"),
Species2 = structure(c(2L, 9L, 1L, 4L, 5L, 7L, 11L, 12L,
13L, 2L, 1L, 4L, 5L, 13L, 2L, 9L, 4L, 5L, 6L, 10L, 8L, 7L,
11L, 13L), .Label = c("Arcitalitrus sp1", "Armadillidae sp1 ",
"Brachyiulus pusillus ", "Dalodesmidae sp1", "Diplopoda",
"Isocladosoma pallidulum ", "Ommatoiulus moreleti ", "Philosciidae sp2",
"Porcellionidae sp1", "Siphonotidae sp2", "Somethus sp1",
"Styloniscidae ", "Styloniscidae sp1"), class = "factor"),
Taxa = structure(c(3L, 3L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L,
1L, 2L, 2L, 3L, 3L, 3L, 2L, 2L, 2L, 2L, 3L, 2L, 2L, 3L), .Label = c("Amphipoda",
"Diplopoda", "Isopoda"), class = "factor"), Variable = structure(c(2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L), .Label = c("Autumn", "Litter",
"Spring", "Summer"), class = "factor"), Coef = c(1.911502938,
2.086917154, 1.571872993, 12.61184801, 15.6161116, -1.430032837,
-12.51944478, 12.33934516, -8.040249562, 8.08258816, 1.780142396,
12.88982576, 16.78107544, -13.22641153, 1.68810887, 2.093965381,
12.27209197, 15.08328526, -6.334640911, -11.29985948, -11.62658947,
-1.676293808, -6.246555908, -3.470297147), SE = c(0.403497472,
2.21607562, 0.348600794, 2.423896379, 0.509468128, 3.423013791,
2.382857733, 1.775086895, 2.087788334, 2.23631504, 0.33402261,
2.518562443, 0.459720131, 1.950974996, 0.2476205, 0.235648095,
1.815155489, 0.325804415, 2.564680067, 2.437104984, 2.212583358,
2.677618401, 2.324019051, 0.420436743), Test.stat = c(18.36532749,
13.27324683, 13.29039037, 20.50277493, 44.06097153, 10.55234932,
14.64951518, 13.22575401, 20.16415411, 16.55627107, 11.81407568,
15.15213717, 40.67205188, 12.62233207, 37.60085488, 16.90879258,
20.20215107, 80.30520371, 13.35250626, 13.01692428, 17.52987519,
20.03658771, 12.02467914, 53.5052683)), row.names = 10:33, class = "data.frame")

Answer 1

This solution is based on grobs: find positions of "strip-l" (left strips) and then substitute the rect grobs with line grobs.
p <- posthoc1 %>%
mutate(ordering = -as.numeric(Dataset) + Test.stat,
Species2 = fct_reorder(Species2, ordering, .desc = F)) %>%
ggplot(aes(x=Coef, y=Species2, reorder(Coef, Taxa), group=Species2, colour=Taxa)) +
geom_point(size=posthoc1$Test.stat*.25, show.legend = FALSE) +
ylab("") +
theme_classic(base_size = 20) +
facet_grid(Taxa~Dataset, scales = "free_y", space = "free_y", switch = "y") +
geom_vline(xintercept = 0) +
theme(axis.text.x=element_text(colour = "black"),
strip.placement = "outside",
#strip.background.x=element_rect(color = "white", fill=NULL),
strip.background.y=element_rect(color = NA)
) +
coord_cartesian(clip = "off") +
scale_x_continuous(limits=NULL)
library(grid)
q <- ggplotGrob(p)
lg <- linesGrob(x=unit(c(0,0),"npc"), y=unit(c(0,1),"npc"),
gp=gpar(col="red", lwd=4))
for (k in grep("strip-l",q$layout$name)) {
q$grobs[[k]]$grobs[[1]]$children[[1]] <- lg
}
grid.draw(q)