While I'm not sure exactly what you want, my guess is that you could first gather all variables into 1 column, and have another column to indicate what variable that is, then create a binary color column, and then plot it, plotting the value onto color, and variable onto, let's say, shape.
You'd also want to use geom_jitter() since your x is Country and your y is Year, but you have 4 observations for each country-year pair, and thus will have 4 overlapping data points.
library(tidyverse)
BP_Stats_Data %>%
gather(var, value, -c(Country, Year)) %>%
mutate(color = if_else(value == 0, '0', '1')) %>%
ggplot(mapping=aes(x = Country,
y= Year,
col = color,
shape = var)) +
geom_jitter() +
scale_color_manual(values = c("0" = "grey", "1" = "blue"))
You could also map var to facet_wrap() and have 4 distinct charts (1 for each variable). I think I'd personally prefer that over shape